On the Gelfand-Hille theorems

Jaroslav Zemánek

Banach Center Publications (1994)

  • Volume: 30, Issue: 1, page 369-385
  • ISSN: 0137-6934

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Zemánek, Jaroslav. "On the Gelfand-Hille theorems." Banach Center Publications 30.1 (1994): 369-385. <http://eudml.org/doc/262822>.

@article{Zemánek1994,
author = {Zemánek, Jaroslav},
journal = {Banach Center Publications},
keywords = {Gelfand-Hille theorems},
language = {eng},
number = {1},
pages = {369-385},
title = {On the Gelfand-Hille theorems},
url = {http://eudml.org/doc/262822},
volume = {30},
year = {1994},
}

TY - JOUR
AU - Zemánek, Jaroslav
TI - On the Gelfand-Hille theorems
JO - Banach Center Publications
PY - 1994
VL - 30
IS - 1
SP - 369
EP - 385
LA - eng
KW - Gelfand-Hille theorems
UR - http://eudml.org/doc/262822
ER -

References

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  1. N. I. Akhiezer [1951], The work of academician S. N. Bernšteĭn on the constructive theory of functions (on the occasion of his seventieth birthday), Uspekhi Mat. Nauk 6, no. 1, 3-67 (in Russian). 
  2. G. R. Allan [1989], Power-bounded elements in a Banach algebra and a theorem of Gelfand, in: Conference on Automatic Continuity and Banach Algebras (Canberra, January 1989), R. J. Loy (ed.), Proc. Centre Math. Anal. Austral. Nat. Univ. 21, 1-12. 
  3. G. R. Allan and T. J. Ransford [1989], Power-dominated elements in a Banach algebra, Studia Math. 94, 63-79. Zbl0705.46021
  4. N. U. Arakelyan and V. A. Martirosyan [1991], Power Series: Analytic Extension and Localization of Singularities, University of Erevan, Erevan (in Russian). Zbl0626.30002
  5. W. Arendt [1983], Spectral properties of Lamperti operators, Indiana Univ. Math. J. 32, 199-215. Zbl0488.47016
  6. W. Arendt and C. J. K. Batty [1988], Tauberian theorems and stability of one-parameter semigroups, Trans. Amer. Math. Soc. 306, 837-852. Zbl0652.47022
  7. A. Atzmon [1980], Operators which are annihilated by analytic functions and invariant subspaces, Acta Math. 144, 27-63. Zbl0449.47007
  8. A. Atzmon [1983], Operators with resolvent of bounded characteristic, Integral Equations Operator Theory 6, 779-803. Zbl0545.47005
  9. A. Atzmon [1984], On the existence of hyperinvariant subspaces, J. Operator Theory 11, 3-40. Zbl0583.47009
  10. A. Atzmon [1993], Unicellular and non-unicellular dissipative operators, Acta Sci. Math. (Szeged) 57, 45-54. Zbl0814.47046
  11. A. Atzmon [in preparation], On the asymptotic growth of the sequence T n + 1 - T n n = 1 for some operators T with σ(T) = 1. 
  12. B. Aupetit [1991], A Primer on Spectral Theory, Springer, New York. 
  13. B. Aupetit and D. Drissi [1994], Some spectral inequalities involving generalized scalar operators, Studia Math. 109, 51-66. Zbl0829.47002
  14. B. Aupetit and J. Zemánek [1981], Local behaviour of the spectral radius in Banach algebras, J. London Math. Soc. 23, 171-178. Zbl0432.46045
  15. B. Aupetit and J. Zemánek [1983], Local behavior of the spectrum near algebraic elements, Linear Algebra Appl. 52/53, 39-44. Zbl0518.46035
  16. B. Aupetit and J. Zemánek [1990], A characterization of normal matrices by their exponentials, ibid. 132, 119-121; 180 (1993), 1-2. Zbl0701.15021
  17. B. A. Barnes [1989], Operators which satisfy polynomial growth conditions, Pacific J. Math. 138, 209-219. Zbl0693.47001
  18. H. Bateman, A. Erdélyi et al. [1953], Higher Transcendental Functions II, McGraw-Hill, New York. Zbl0143.29202
  19. C. J. K. Batty [1994a], Some Tauberian theorems related to operator theory, this volume, 21-34. Zbl0810.40005
  20. C. J. K. Batty [1994b], Asymptotic behaviour of semigroups of operators, this volume, 35-52. Zbl0818.47034
  21. B. Beauzamy [1987], Orbites tendant vers l'infini, C. R. Acad. Sci. Paris Sér. I Math. 305, 123-126. Zbl0615.47003
  22. B. Beauzamy [1988], Introduction to Operator Theory and Invariant Subspaces, North-Holland, Amsterdam. Zbl0663.47002
  23. M. Berkani [1983], Inégalités et Propriétés Spectrales dans les Algèbres de Banach, Thèse, Université de Bordeaux I, Bordeaux. 
  24. A. Bernard [1971], Algèbres quotients d'algèbres uniformes, C. R. Acad. Sci. Paris Sér. A-B 272, A1101-A1104. Zbl0222.46034
  25. S. J. Bernau and C. B. Huijsmans [1990], On the positivity of the unit element in a normed lattice ordered algebra, Studia Math. 97, 143-149. Zbl0782.47031
  26. S. Bernstein [1923], Sur une propriété des fonctions entières, C. R. Acad. Sci. Paris 176, 1603-1605. Zbl49.0215.02
  27. A. Beurling [1938], Sur les intégrales de Fourier absolument convergentes et leur application à une transformation fonctionnelle, in: Ninth Scandinavian Math. Congress, Helsingfors, 345-366. Also in: Collected Works of Arne Beurling, Vol. 2, Harmonic Analysis, L. Carleson, P. Malliavin, J. Neuberger, and J. Wermer (eds.), Birkhäuser, Boston, 1989, 39-60. 
  28. L. Bieberbach [1927], Lehrbuch der Funktionentheorie II, Teubner, Berlin. Zbl53.0277.08
  29. L. Bieberbach [1955], Analytische Fortsetzung, Springer, Berlin. Zbl0064.06902
  30. R. P. Boas, Jr. [1954], Entire Functions, Academic Press, New York. Zbl66.0355.01
  31. R. P. Boas, Jr. [1969], Inequalities for the derivatives of polynomials, Math. Mag. 42, 165-174. F. F. Bonsall and M. J. Crabb [1970], The spectral radius of a Hermitian element of a Banach algebra, Bull. London Math. Soc. 2, 178-180. 
  32. F. F. Bonsall and J. Duncan [1971], Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras, Cambridge University Press, Cambridge. Zbl0207.44802
  33. F. F. Bonsall and J. Duncan [1973], Complete Normed Algebras, Springer, Berlin. Zbl0271.46039
  34. A. Browder [1969], States, numerical ranges, etc., Proc. Brown Univ. Informal Analysis Seminar, Providence. 
  35. A. Browder [1971], On Bernstein's inequality and the norm of Hermitian operators, Amer. Math. Monthly 78, 871-873. Zbl0224.47011
  36. A. Brunel et R. Émilion [1984], Sur les opérateurs positifs à moyennes bornées, C. R. Acad. Sci. Paris Sér. I Math. 298, 103-106. Zbl0582.47038
  37. A. L. Bukhgeĭm [1988], Introduction to the Theory of Inverse Problems, Nauka, Novosibirsk (in Russian). 
  38. L. Burlando [1994], Characterizations of nilpotent operators, letter. Zbl0802.46062
  39. L. Collatz [1963], Eigenwertaufgaben mit technischen Anwendungen, Geest & Portig, Leipzig. 
  40. E. F. Collingwood and A. J. Lohwater [1966], The Theory of Cluster Sets, Cambridge University Press, Cambridge. Zbl0149.03003
  41. I. Colojoară and C. Foiaş [1968], Theory of Generalized Spectral Operators, Gordon and Breach, New York. Zbl0189.44201
  42. J. W. Daniel and T. W. Palmer [1969], On σ(T), ∥T∥, and T - 1 , Linear Algebra Appl. 2, 381-386. 
  43. Y. Derriennic and M. Lin [1973], On invariant measures and ergodic theorems for positive operators, J. Funct. Anal. 13, 252-267. Zbl0262.28011
  44. P. Dienes [1931], The Taylor Series, Oxford University Press, Oxford. Zbl0003.15502
  45. W. F. Donoghue, Jr. [1963], On a problem of Nieminen, Inst. Hautes Études Sci. Publ. Math. 16, 127-129. 
  46. R. S. Doran and V. A. Belfi [1986], Characterizations of C*-Algebras, Marcel Dekker, New York. 
  47. N. Dunford [1943], Spectral theory. I. Convergence to projections, Trans. Amer. Math. Soc. 54, 185-217. Zbl0063.01185
  48. R. Emilion [1985], Mean-bounded operators and mean ergodic theorems, J. Funct. Anal. 61, 1-14. Zbl0562.47007
  49. J. Esterle [1983], Quasimultipliers, representations of H , and the closed ideal problem for commutative Banach algebras, in: Radical Banach Algebras and Automatic Continuity (Long Beach, Calif., 1981), J. M. Bachar, W. G. Bade, P. C. Curtis Jr., H. G. Dales, and M. P. Thomas (eds.), Lecture Notes in Math. 975, Springer, 66-162. 
  50. J. Esterle [1994], Uniqueness, strong forms of uniqueness and negative powers of contractions, this volume, 127-145. Zbl0893.46043
  51. G. Faber [1903], Über die Fortsetzbarkeit gewisser Taylorscher Reihen, Math. Ann. 57, 369-388. Zbl34.0432.01
  52. C. Fernandez-Pujol [1988], Séries convergentes d'opérateurs dans un espace de Banach, C. R. Acad. Sci. Paris Sér. I Math. 306, 331-334. Zbl0646.47027
  53. I. Gelfand [1941a], Ideale und primäre Ideale in normierten Ringen, Mat. Sb. 9, 41-48. Zbl67.0406.03
  54. I. Gelfand [1941b], Zur Theorie der Charactere der Abelschen topologischen Gruppen, ibid. 9, 49-50. Zbl67.0407.02
  55. A. G. Gibson [1972], A discrete Hille-Yosida-Phillips theorem, J. Math. Anal. Appl. 39, 761-770. Zbl0213.14504
  56. I. Gohberg, S. Goldberg and M. A. Kaashoek [1990], Classes of Linear Operators I, Birkhäuser, Basel. Zbl0745.47002
  57. I. C. Gohberg and M. G. Kreĭn [1969], Introduction to the Theory of Linear Nonselfadjoint Operators, Amer. Math. Soc., Providence. Zbl0181.13504
  58. S. Grabiner [1971], Ranges of quasi-nilpotent operators, Illinois J. Math. 15, 150-152. Zbl0204.45003
  59. S. Grabiner [1974], Ranges of products of operators, Canad. J. Math. 26, 1430-1441. Zbl0259.47003
  60. S. Grabiner [1979], Operator ranges and invariant subspaces, Indiana Univ. Math. J. 28, 845-857. Zbl0456.47006
  61. S. Grabiner [1982], Uniform ascent and descent of bounded operators, J. Math. Soc. Japan 34, 317-337. Zbl0477.47013
  62. P. R. Halmos [1967], A Hilbert Space Problem Book, Von Nostrand, Princeton. 
  63. E. Hille [1944], On the theory of characters of groups and semi-groups in normed vector rings, Proc. Nat. Acad. Sci. U.S.A. 30, 58-60. Zbl0061.25305
  64. E. Hille [1962], Analytic Function Theory II, Ginn, Boston. Zbl0102.29401
  65. E. Hille and R. S. Phillips [1957], Functional Analysis and Semi-Groups, Amer. Math. Soc., Providence. Zbl0078.10004
  66. R. A. Hirschfeld [1968], On semi-groups in Banach algebras close to the identity, Proc. Japan Acad. 44, 755. Zbl0172.40904
  67. V. I. Istrăţescu [1978], Topics in Linear Operator Theory, Academia Nazionale dei Lincei, Roma. 
  68. B. Johnson [1971], Continuity of operators commuting with quasi-nilpotent operators, Indiana Univ. Math. J. 20, 913-915. Zbl0209.44903
  69. L. K. Jones and M. Lin [1980], Unimodular eigenvalues and weak mixing, J. Funct. Anal. 35, 42-48. Zbl0441.47009
  70. M. A. Kaashoek [1969], Locally compact semi-algebras and spectral theory, Nieuw Arch. Wisk. 17, 8-16. Zbl0183.42003
  71. M. A. Kaashoek and T. T. West [1968], Locally compact monothetic semi-algebras, Proc. London Math. Soc. 18, 428-438. Zbl0162.18601
  72. M. A. Kaashoek and T. T. West [1974], Locally Compact Semi-Algebras with Applications to Spectral Theory of Positive Operators, North-Holland, Amsterdam. Zbl0288.46043
  73. S. Kantorovitz [1965], Classification of operators by means of their operational calculus, Trans. Amer. Math. Soc. 115, 194-224. Zbl0127.07801
  74. V. È] . Katsnel'son [1970], Conservative operator has norm equal to its spectral radius, Mat. Issled. 5, no. 3, 186-189 (in Russian). Zbl0226.47002
  75. Y. Katznelson and L. Tzafriri [1986], On power bounded operators, J. Funct. Anal. 68, 313-328. Zbl0611.47005
  76. L. Kérchy [1994], Unitary asymptotes of Hilbert space operators, this volume, 191-201. Zbl0807.47005
  77. K. Knopp [1947], Theorie und Anwendung der unendlichen Reihen, Springer, Berlin. Zbl0031.11801
  78. J. J. Koliha [1974a], Some convergence theorems in Banach algebras, Pacific J. Math. 52, 467-473. Zbl0265.46049
  79. J. J. Koliha [1974b], Power convergence and pseudoinverses of operators in Banach spaces, J. Math. Anal. Appl. 48, 446-469. Zbl0292.47003
  80. J. Korevaar [1948], Entire functions of exponential type, Math. Centrum Amsterdam, Rapport ZW 1948-011, 10 pp. (in Dutch). 
  81. J. Korevaar [1949a], Functions of exponential type bounded on sequences of points, Ann. Soc. Polon. Math. 22, 207-234. Zbl0035.34001
  82. J. Korevaar [1949b], A simple proof of a theorem of Pólya, Simon Stevin 26, 81-89. Zbl0032.06701
  83. E. Landau [1946], Darstellung und Begründung einiger neuerer Ergebnisse der Funktionentheorie, Chelsea, New York. 
  84. D. C. Lay [1970], Spectral analysis using ascent, descent, nullity and defect, Math. Ann. 184, 197-214. Zbl0177.17102
  85. G. K. Leaf [1963], A spectral theory for a class of linear operators, Pacific J. Math. 13, 141-155. Zbl0121.33502
  86. L. Leau [1899], Recherches sur les singularités d'une fonction définie par un développement de Taylor, J. Math. Pures Appl. 5, 365-425. Zbl30.0368.04
  87. E. Le Roy [1900], Sur les séries divergentes et les fonctions définies par un développement de Taylor, Ann. Fac. Sci. Toulouse Math. 2, 317-430. 
  88. B. Ja. Levin [1964], Distribution of Zeros of Entire Functions, Amer. Math. Soc., Providence. 
  89. E. Lindelöf [1905], Le Calcul des Résidus, et ses Applications à la Théorie des Fonctions, Gauthier-Villars, Paris. Zbl36.0468.01
  90. E. R. Lorch [1941], The integral representation of weakly almost-periodic transformations in reflexive vector spaces, Trans. Amer. Math. Soc. 49, 18-40. Zbl67.0415.01
  91. C. Lubich and O. Nevanlinna [1991], On resolvent conditions and stability estimates, BIT 31, 293-313. Zbl0731.65043
  92. G. Lumer [1961], Semi-inner-product spaces, Trans. Amer. Math. Soc. 100, 29-43. Zbl0102.32701
  93. G. Lumer [1964], Spectral operators, hermitian operators, and bounded groups, Acta Sci. Math. (Szeged) 25, 75-85. Zbl0168.12103
  94. G. Lumer [1971], Bounded groups and a theorem of Gelfand, Rev. Un. Mat. Argentina 25, 239-245. Zbl0324.46047
  95. G. Lumer and R. S. Phillips [1961], Dissipative operators in a Banach space, Pacific J. Math. 11, 679-698. Zbl0101.09503
  96. Yu. I. Lyubich and Vũ Quôc Phóng [1988], Asymptotic stability of linear differential equations in Banach spaces, Studia Math. 88, 37-42. 
  97. A. I. Markushevich [1976], Selected Chapters in the Theory of Analytic Functions, Nauka, Moscow (in Russian). Zbl0459.30001
  98. M. Mbekhta et J. Zemánek [1993], Sur le théorème ergodique uniforme et le spectre, C. R. Acad. Sci. Paris Sér. I Math. 317, 1155-1158. 
  99. C. A. McCarthy [1971], A strong resolvent condition does not imply power-boundedness, Chalmers Institute of Technology and the University of Göteborg, Preprint no. 15, Göteborg. 
  100. C. A. McCarthy and J. Schwartz [1965], On the norm of a finite Boolean algebra of projections, and applications to theorems of Kreiss and Morton, Comm. Pure Appl. Math. 18, 191-201. Zbl0151.19401
  101. P. Meyer-Nieberg [1991], Banach Lattices, Springer, Berlin. Zbl0743.46015
  102. A. Mokhtari [1988], Distance entre éléments d'un semi-groupe continu dans une algèbre de Banach, J. Operator Theory 20, 375-380. Zbl0713.46034
  103. V. Müller [1994], Local behaviour of operators, this volume, 251-258. Zbl0820.47001
  104. O. Nevanlinna [1993], Convergence of Iterations for Linear Equations, Birkhäuser, Basel. Zbl0846.47008
  105. T. Nieminen [1962], A condition for the self-adjointness of a linear operator, Ann. Acad. Sci. Fenn. Ser. A I No. 316, 5 pp. Zbl0171.34502
  106. J. I. Nieto [1982], Opérateurs à itérés uniformément bornés, Canad. Math. Bull. 25, 355-360. Zbl0524.47004
  107. N. K. Nikol'skiĭ [1977], A Tauberian theorem for the spectral radius, Siberian Math. J. 18, 969-972. 
  108. K. Noshiro [1960], Cluster Sets, Springer, Berlin. 
  109. N. Obreschkoff [1934], Lösung der Aufgabe 106, Jahresber. Deutsch. Math.-Verein. 43, 2. Abt., 13-15. 
  110. R. E. A. C. Paley and N. Wiener [1934], Fourier Transforms in the Complex Domain, Amer. Math. Soc., New York. Zbl0011.01601
  111. A. Pazy [1983], Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York. Zbl0516.47023
  112. D. Petz [1994], A survey of certain trace inequalities, this volume, 287-298. Zbl0802.15012
  113. G. Pólya [1931a], Aufgabe 105, Jahresber. Deutsch. Math.-Verein. 40, 2. Abt., 80. 
  114. G. Pólya [1931b], Aufgabe 106, ibid., 81. 
  115. G. Pólya [1974], Collected Papers, Vol. I, Singularities of Analytic Functions, R. P. Boas (ed.), The MIT Press, Cambridge, Mass. 
  116. G. Pólya und G. Szegö [1964], Aufgaben und Lehrsätze aus der Analysis, Springer, Berlin. Zbl0122.29704
  117. A. Pringsheim [1929], Kritisch-historische Bemerkungen zur Funktionentheorie, Sitzungsber. Bayer. Akad. Wiss. München, Math.-Natur. Abt., 95-124. Zbl55.0760.01
  118. A. Pringsheim [1932], Vorlesungen über Funktionenlehre II.2, Teubner, Leipzig. Zbl58.0296.18
  119. I. I. Privalov [1950], Boundary Properties of Analytic Functions, GITTL, Moscow (in Russian). 
  120. D. Przeworska-Rolewicz and S. Rolewicz [1987], The only continuous Volterra right inverses in C c [ 0 , 1 ] of the operator d/dt are a t , Colloq. Math. 51, 281-285. Zbl0636.47028
  121. V. Pták [1976], The spectral radii of an operator and its modulus, Comment. Math. Univ. Carolin. 17, 273-279. Zbl0332.15003
  122. T. Pytlik [1987], Analytic semigroups in Banach algebras and a theorem of Hille, Colloq. Math. 51, 287-294. Zbl0632.46043
  123. H. Radjavi and P. Rosenthal [1973], Invariant Subspaces, Springer, Berlin. Zbl0269.47003
  124. M. Reed and B. Simon [1972], Methods of Modern Mathematical Physics, Vol. 1, Functional Analysis, Academic Press, New York. Zbl0242.46001
  125. R. Remmert [1991], Theory of Complex Functions, Springer, New York. Zbl0780.30001
  126. R. K. Ritt [1953], A condition that l i m n n - 1 T n = 0 , Proc. Amer. Math. Soc. 4, 898-899. 
  127. S. Rolewicz [1969], On orbits of elements, Studia Math. 32, 17-22. Zbl0174.44203
  128. H. C. Rönnefarth [1993], Charakterisierung des Verhaltens der Potenzen eines Elementes einer Banach-Algebra durch Spektraleigenschaften, Diplomarbeit, Technische Universität Berlin, Berlin, 77 pp. 
  129. G. Sansone [1959], Orthogonal Functions, Interscience, New York. Zbl0084.06106
  130. R. Sato [1979], The Hahn-Banach theorem implies Sine's mean ergodic theorem, Proc. Amer. Math. Soc. 77, 426. Zbl0434.47010
  131. R. Sato [1981], On a mean ergodic theorem, ibid. 83, 563-564. Zbl0469.47012
  132. H. H. Schaefer [1974], Banach Lattices and Positive Operators, Springer, Berlin. Zbl0296.47023
  133. C. Schmoeger [1993], On isolated points of the spectrum of a bounded linear operator, Proc. Amer. Math. Soc. 117, 715-719. Zbl0780.47019
  134. S. L. Segal [1981], Nine Introductions in Complex Analysis, North-Holland, Amsterdam. Zbl0482.30002
  135. S. M. Shah [1946], On the singularities of a class of functions on the unit circle, Bull. Amer. Math. Soc. 52, 1053-1056. Zbl0061.14603
  136. S.-Y. Shaw [1980], Ergodic projections of continuous and discrete semigroups, Proc. Amer. Math. Soc. 78, 69-76. Zbl0394.47020
  137. A. L. Shields [1978], On Möbius bounded operators, Acta Sci. Math. (Szeged) 40, 371-374. Zbl0358.47025
  138. G. E. Shilov [1950], On a theorem of I. M. Gel'fand and its generalizations, Dokl. Akad. Nauk SSSR 72, 641-644 (in Russian). Zbl0039.33601
  139. V. S. Shul'man [1994], Invariant subspaces and spectral mapping theorems, this volume, 313-325. 
  140. A. M. Sinclair [1971], The norm of a Hermitian element in a Banach algebra, Proc. Amer. Math. Soc. 28, 446-450. Zbl0242.46035
  141. R. Sine [1969], A note on rays at the identity operator, ibid. 23, 546-547. Zbl0186.19203
  142. R. Sine [1970], A mean ergodic theorem, ibid. 24, 438-439. Zbl0191.42204
  143. B. M. Solomyak [1982], The existence of invariant subspaces for operators with nonsymmetric growth of the resolvent, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 107, 204-208, 233-234 (in Russian). Zbl0531.47005
  144. B. M. Solomyak [1983], Calculuses, annihilators and hyperinvariant subspaces, J. Operator Theory 9, 341-370. Zbl0617.47003
  145. J. G. Stampfli [1967], An extreme point theorem for inverses in a Banach algebra with identity, Proc. Cambridge Philos. Soc. 63, 993-994. Zbl0185.38602
  146. J. G. Stampfli and J. P. Williams [1968], Growth conditions and the numerical range in a Banach algebra, Tôhoku Math. J. 20, 417-424. Zbl0175.43902
  147. M. H. Stone [1948], On a theorem of Pólya, J. Indian Math. Soc. 12, 1-7. Zbl0031.05702
  148. J. C. Strikwerda [1989], Finite Difference Schemes and Partial Differential Equations, Wadsworth & Brooks/Cole, Pacific Grove, Calif. Zbl0681.65064
  149. J. C. Strikwerda and B. A. Wade [1991], Cesàro means and the Kreiss matrix theorem, Linear Algebra Appl. 145, 89-106. Zbl0724.15021
  150. A. Święch [1990], Spectral characterization of operators with precompact orbit, Studia Math. 96, 277-282; 97, 266. Zbl0725.47003
  151. G. Szegö [1934], Lösung der Aufgabe 105, Jahresber. Deutsch. Math.-Verein. 43, 2. Abt., 10-11. 
  152. G. Szegö [1959], Orthogonal Polynomials, Amer. Math. Soc., New York. Zbl0089.27501
  153. B. Sz.-Nagy [1947], On uniformly bounded linear transformations in Hilbert space, Acta Sci. Math. (Szeged) 11, 152-157. 
  154. A. E. Taylor and D. C. Lay [1980], Introduction to Functional Analysis, Wiley, New York. Zbl0501.46003
  155. E. C. Titchmarsh [1939], The Theory of Functions, Oxford University Press. Zbl0022.14602
  156. F. G. Tricomi [1955], Vorlesungen über Orthogonalreihen, Springer, Berlin. Zbl0065.29601
  157. L. Tschakaloff [1934], Zweite Lösung der Aufgabe 105, Jahresber. Deutsch. Math.-Verein. 43, 2. Abt., 11-13. 
  158. G. Valiron [1925], Sur la formule d'interpolation de Lagrange, Bull. Sci. Math. 49, 181-192, 203-224. Zbl51.0250.02
  159. G. Valiron [1954], Fonctions Analytiques, Presses Universitaires de France, Paris. 
  160. J. A. Van Casteren [1985], Generators of Strongly Continuous Semigroups, Pitman, London. Zbl0576.47023
  161. I. Vidav [1956], Eine metrische Kennzeichnung der selbstadjungierten Operatoren, Math. Z. 66, 121-128. Zbl0071.11503
  162. I. Vidav [1982], Linear Operators in Banach Spaces, Društvo Matematikov, Fizikov in Astronomov SR Slovenije, Ljubljana (in Slovenian). 
  163. Vũ Quôc Phóng [1992], A short proof of the Y. Katznelson's and L. Tzafriri's theorem, Proc. Amer. Math. Soc. 115, 1023-1024. Zbl0781.47003
  164. Vũ Quôc Phóng [1993], Semigroups with nonquasianalytic growth, Studia Math. 104, 229-241. Zbl0813.47047
  165. H.-D. Wacker [1985], Über die Verallgemeinerung eines Ergodensatzes von Dunford, Arch. Math. (Basel) 44, 539-546. Zbl0555.47008
  166. L. J. Wallen [1967], On the magnitude of x n - 1 in a normed algebra, Proc. Amer. Math. Soc. 18, 956. Zbl0172.40903
  167. J. Wermer [1952], The existence of invariant subspaces, Duke Math. J. 19, 615-622. Zbl0047.35806
  168. D. V. Widder [1941], The Laplace Transform, Princeton University Press, Princeton. Zbl0063.08245
  169. S. Wigert [1900], Sur les fonctions entières, Öfversigt af Kongl. Vetenskaps-Akademiens Förhandlingar, Stockholm, No. 8, 1001-1011. 
  170. W. Wils [1969], On semigroups near the identity, Proc. Amer. Math. Soc. 21, 762-763. Zbl0181.41002
  171. F. Wolf [1957], Operators in Banach space which admit a generalized spectral decomposition, Indag. Math. 19, 302-311. Zbl0077.31701
  172. N. J. Young [1978], Analytic programmes in matrix algebras, Proc. London Math. Soc. 36, 226-242. Zbl0379.65023
  173. B. Zalar [1993], History of the Vidav theorem, Obzornik Mat. Fiz. 40, 9-14 (in Slovenian). Zbl0763.46001
  174. M. Zarrabi [1993], Contractions à spectre dénombrable et propriétés d'unicité des fermés dénombrables du cercle, Ann. Inst. Fourier (Grenoble) 43, 251-263. 
  175. M. Zarrabi [to appear], Spectral synthesis and applications to C₀-groups, J. Austral. Math. Soc. Ser. A. Zbl0854.47026
  176. J. Zemánek [à paraître], Sur les itérations des opérateurs, Publ. Math. Univ. Pierre et Marie Curie, Séminaire d'Initiation à l'Analyse. 
  177. X.-D. Zhang [1992], Two simple proofs of a theorem of Schaefer, Wolff and Arendt 

Citations in EuDML Documents

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  1. Sen Huang, Characterizing spectra of closed operators through existence of slowly growing solutions of their Cauchy problems
  2. Yu. Lyubich, J. Zemánek, Precompactness in the uniform ergodic theory
  3. J. van Casteren, Boundedness properties of resolvents and semigroups of operators
  4. Graham Allan, Sums of idempotents and a lemma of N. J. Kalton
  5. Driss Drissi, On a generalization of Lumer-Phillips' theorem for dissipative operators in a Banach space
  6. Michael Lin, The uniform zero-two law for positive operators in Banach lattices
  7. Olavi Nevanlinna, On the growth of the resolvent operators for power bounded operators
  8. Helmuth Rönnefarth, On the differences of the consecutive powers of Banach algebra elements
  9. Laura Burlando, A generalization of the uniform ergodic theorem to poles of arbitrary order
  10. Zoltán Léka, A note on the powers of Cesàro bounded operators

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