Operator semigroups in Banach space theory

Pietro Aiena; Manuel González; Antonio Martínez-Abejón

Bollettino dell'Unione Matematica Italiana (2001)

  • Volume: 4-B, Issue: 1, page 157-205
  • ISSN: 0392-4041

How to cite


Aiena, Pietro, González, Manuel, and Martínez-Abejón, Antonio. "Operator semigroups in Banach space theory." Bollettino dell'Unione Matematica Italiana 4-B.1 (2001): 157-205. <http://eudml.org/doc/195424>.

author = {Aiena, Pietro, González, Manuel, Martínez-Abejón, Antonio},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {157-205},
publisher = {Unione Matematica Italiana},
title = {Operator semigroups in Banach space theory},
url = {http://eudml.org/doc/195424},
volume = {4-B},
year = {2001},

AU - Aiena, Pietro
AU - González, Manuel
AU - Martínez-Abejón, Antonio
TI - Operator semigroups in Banach space theory
JO - Bollettino dell'Unione Matematica Italiana
DA - 2001/2//
PB - Unione Matematica Italiana
VL - 4-B
IS - 1
SP - 157
EP - 205
LA - eng
UR - http://eudml.org/doc/195424
ER -


  1. AIENA, P., An internal characterization of inessential operators, Proc. Amer. Math. Soc., 102 (1988), 625-626. Zbl0691.47024MR928992
  2. AIENA, P., On Riesz and inessential operators, Math. Z., 201 (1989), 521-528. Zbl0702.47008MR1004172
  3. AIENA, P.- GONZÁLEZ, M., Essentially incomparable Banach spaces and Fredholm theory, Proc. R. Ir. Acad. A, 93 (1993), 49-59. Zbl0790.46010MR1241839
  4. AIENA, P.- GONZÁLEZ, M., On the perturbation classes of semi-Fredholm and Fredholm operators, Rendiconti Circ. Mat. Palermo Suppl., 40 (1996), 37-46. Zbl0882.47002MR1407075
  5. AIENA, P.- GONZÁLEZ, M., On inessential and improjective operators, Studia Math., 131 (1998), 271-287. Zbl0937.47013MR1644476
  6. AIENA, P.- GONZÁLEZ, M., Examples of improjective operators, Math. Z., to appear. Zbl0960.47009MR1750932
  7. AIENA, P.- GONZÁLEZ, M.- MARTÍNEZ-ABEJÓN, A., Incomparable Banach spaces and semigroups of operators, Preprint, 1999. 
  8. AIENA, P.- GONZÁLEZ, M.- MARTÍNEZ-ABEJÓN, A., On the operators which are invertible modulo an operator ideal, Preprint, 1999. Zbl1010.47044MR1860060
  9. ALVAREZ, T.- GONZÁLEZ, M., Some examples of tauberian operators, Proc. Amer. Math. Soc., 111 (1991), 1023-1027. Zbl0733.47017MR1033955
  10. ALVAREZ, T.- GONZÁLEZ, M.- ONIEVA, V. M., Totally incomparable Banach spaces and three-space ideals, Math. Nachr., 131 (1987), 83-88. Zbl0659.46009MR908801
  11. ALVAREZ, T.- GONZÁLEZ, M.- ONIEVA, V. M., Characterizing two classes of operator ideals, in Contribuciones Matemáticas. Homenaje Prof. Antonio Plans, Univ. Zaragoza 1990, 7-21. 
  12. ASTALA, K., On measures of noncompactness and ideal variations in Banach spaces, Ann. Acad. Sci. Fennicae Ser. A I Math., Dissertationes, 29 (1980), 42 pp. Zbl0426.47001MR575533
  13. ASTALA, K.- TYLLI, H.-O., Seminorms related to weak compactness and to tauberian operators, Math. Proc. Cambridge Phil. Soc., 107 (1990), 365-375. Zbl0709.47009MR1027789
  14. ATKINSON, F., Relatively regular operators, Acta Sci. Math. Szeged, 15 (1953), 38-56. Zbl0052.12502MR56835
  15. BASALLOTE, M., Representabilidad finita por cocientes y operadores, Doctoral Thesis, Univ. Sevilla, 1998. 
  16. BEAUZAMY, B., Opérateurs uniformément convexifiants, Studia Math., 57 (1976), 1023-1027. Zbl0372.46016MR430844
  17. BEAUZAMY, B., Introduction to Banach spaces and their Geometry, North Holland68, 1985. Zbl0585.46009MR889253
  18. BELLENOT, S., The J -sum of Banach spaces, J. Funct. Anal., 48 (1982), 95-106. Zbl0494.46015MR671317
  19. BOMBAL, F.- FIERRO, C., Compacidad débil en espacios de Orlicz de funciones vectoriales, Rev. Real Acad. Ciencias Madrid, 78 (1984), 157-163. Zbl0621.46034MR799701
  20. BOMBAL, F.- HERNANDO, B., A double-dual characterization of Rosenthal and semitauberian operators, Proc. R. Ir. Acad. A, 95 (1995), 69-75. Zbl0856.47003MR1369046
  21. BOURGAIN, J.- ROSENTHAL, H. P., Applications of the theory of semi-embeddings to Banach space theory, J. Funct. Anal., 52 (1983), 149-188. Zbl0541.46020MR707202
  22. BONET, J.- RAMANUJAN, M., Two classes of operators between Fréchet spaces, Functional analysis (Trier 1994), 53-58, de Gruyter, 1996. Zbl0881.47003MR1420437
  23. CARADUS, S.- PFAFFENBERGER, W.- YOOD, B., Calkin algebras and algebras of operators in Banach spaces, M. Dekker Lecture Notes in Pure & Appl. Math.9, 1974. Zbl0299.46062
  24. CASAZZA, P. G.- SHURA, T. J., Tsirelson space, Springer Lectures Notes in Math.1363, 1989. Zbl0709.46008MR981801
  25. CASTILLO, J. M. F.- GONZÁLEZ, M., Three-space problems in Banach space theory, Springer Lecture Notes in Math.1667, 1997. Zbl0914.46015MR1482801
  26. CROSS, R. W., Linear transformations of tauberian type in normed spaces, Note di Mat. volume dedicated to Prof. Köthe (1980), 193-203. Zbl0780.47002MR1193523
  27. CROSS, R. W., On a theorem of Kalton and Wilansky concerning tauberian operators, J. Math. Anal. Appl., 171 (1992), 156-170. Zbl0780.47001MR1192500
  28. CROSS, R. W., A characterisation of almost-reflexive normed spaces, Proc. R. Ir. Acad. A, 92 (1992), 225-228. Zbl0741.46005MR1204221
  29. CROSS, R. W., F + -operators are tauberian, Quaestiones Math., 18 (1995), 129-132. Zbl0804.47001MR1234458
  30. CROSS, R. W., Multivalued linear operators, M. Dekker Pure and Appl. Math. Series213, 1998. Zbl0911.47002MR1631548
  31. DAVIS, W. J.- FIGIEL, T.- JOHNSON, W. B.- PEŁCCZYŃSKI, A., Factoring weakly compact operators, J. Funct. Anal., 19 (1974), 311-327. Zbl0306.46020MR355536
  32. DIESTEL, J.- UHL, J., Vector measures, Amer. Math. Soc., Math. Surveys15, 1977. Zbl0369.46039MR453964
  33. GHOUSSOUB, N., Some remarks concerning G δ -embeddings and semi-quotient maps, Longhorn Notes, Univ. Texas (1982-83), 109-122. MR832220
  34. GHOUSSOUB, N.- MAUREY, B., G δ -embeddings in Hilbert space II, J. Funct. Anal., 78 (1988), 271-305. Zbl0682.46013MR943500
  35. GHOUSSOUB, N.- ROSENTHAL, H.P., Martingales, G δ -embeddings and quotients of L 1 , Math. Ann., 264 (1983), 321-332. Zbl0511.46017MR714107
  36. GOLDBERG, S., Unbounded linear operators, McGraw-Hill, 1966. Zbl0148.12501MR200692
  37. GONZÁLEZ, M., Properties and applications of tauberian operators, Extracta Math., 5 (1990), 91-107. Zbl0748.47001MR1125675
  38. GONZÁLEZ, M., Dual results of factorization for operators, Ann. Acad. Sci. Fennicae, 18 (1993), 3-11. Zbl0795.46013MR1207890
  39. GONZÁLEZ, M., On essentially incomparable Banach spaces, Math. Z., 215 (1994), 621-629. Zbl0791.46011MR1269493
  40. GONZÁLEZ, M.- MARTÍNEZ-ABEJÓN, A., Supertauberian operators and perturbations, Arch. Math., 64 (1995), 423-433. 
  41. GONZÁLEZ, M.- MARTÍNEZ-ABEJÓN, A., Tauberian operators on L 1 μ -spaces, Studia Math., 125 (1997), 289-303. 
  42. GONZÁLEZ, M.- MARTÍNEZ-ABEJÓN, A., Ultrapowers and semi-Fredholm operators, Bolletino U.M.I. B, 11 (1997), 415-433. 
  43. GONZÁLEZ, M.- MARTÍNEZ-ABEJÓN, A., Quotients of L 1 by reflexive subspaces, Extracta Math., 12 (1997), 139-143. 
  44. GONZÁLEZ, M.- MARTÍNEZ-ABEJÓN, A., Lifting unconditionally converging series and semigroups, Bull. Austral. Math. Soc., 57 (1998), 135-146. 
  45. GONZÁLEZ, M.- MARTÍNEZ-ABEJÓN, A., Local reflexivity of dual Banach spaces, Pacific J. Math., 189 (1999), 263-278. 
  46. GONZÁLEZ, M.- MARTÍNEZ-ABEJÓN, A., Tauberian operators on L 1 μ and ultrapowers, Rendiconti Circ. Mat. Palermo Suppl., 56 (1998), 128-138. 
  47. GONZÁLEZ, M.- MARTÍNEZ-ABEJÓN, A., Ultrapowers and semigroups of operators, Integral Equations Operator Theory, to appear. 
  48. GONZÁLEZ, M.- MARTÍNEZ-ABEJÓN, A., Ultrapowers of L 1 μ and the subsequence splitting property, Preprint, 1998. 
  49. GONZÁLEZ, M.- MARTINÓN, A., Operational quantities derived from the norm and measures of noncompactness, Proc. R. Ir. Acad. A, 91 (1991), 63-70. Zbl0760.47021MR1173159
  50. GONZÁLEZ, M.- MARTINÓN, A., Operational quantities derived from the norm and generalized Fredholm theory, Comment. Math. Univ. Carolinae, 32 (1991) 645-657. Zbl0762.47005MR1159811
  51. GONZÁLEZ, M.- MARTINÓN, A., Fredholm theory and space ideals, Boll. U.M.I. B, 7 (1993), 473-488. Zbl0784.47022
  52. GONZÁLEZ, M.- MARTINÓN, A., On incomparability of Banach spaces, Banach Center Publ., 30 (1994), 161-174. Zbl0819.46009
  53. GONZÁLEZ, M.- MARTINÓN, A., Operational quantities characterizing semi-Fredholm operators, Studia Math., 114 (1995), 13-27. Zbl0830.47008MR1330214
  54. GONZÁLEZ, M.- ONIEVA, V. M., On incomparability of Banach spaces, Math. Z., 192 (1986), 581-585. Zbl0602.46015MR847007
  55. GONZÁLEZ, M.- ONIEVA, V. M., Semi-Fredholm operators and semigroups associated with some classical operator ideals, Proc. R. Ir. Acad. A, 88 (1988), 35-38. Zbl0633.47029MR974281
  56. GONZÁLEZ, M.- ONIEVA, V. M., Semi-Fredholm operators and semigroups associated with some classical operator ideals II, Proc. R. Ir. Acad. A, 88 (1988), 119-124. Zbl0645.47038MR986218
  57. GONZÁLEZ, M.- ONIEVA, V. M., Lifting results for sequences in Banach spaces, Math. Proc. Cambridge Phil. Soc., 105 (1989), 117-121. Zbl0633.46025MR966145
  58. GONZÁLEZ, M.- ONIEVA, V. M., Characterizations of tauberian operators and other semigroups of operators, Proc. Amer. Math. Soc., 108 (1990), 399-405. Zbl0704.47016MR994777
  59. GONZÁLEZ, M.- SAKSMAN, E.- TYLLI, H.-O., Representing non-weakly compact operators, Studia Math., 113 (1995), 265-282. Zbl0832.47039MR1330211
  60. GOWERS, W. T., A solution to Banach's hyperplane problem, Bull. London Math. Soc., 26 (1994), 523-530. Zbl0838.46011MR1315601
  61. GOWERS, W. T.- MAUREY, B., The unconditional basic sequence problem, J. Amer. Math. Soc., 6 (1993), 851-874. Zbl0827.46008MR1201238
  62. GROTHENDIECK, A., Sur les applications linéaires faiblement compactes d'espaces du type C K , Canadian J. Math., 5 (1953), 129-173. Zbl0050.10902MR58866
  63. HARTE, R., Invertibility and singularity for bounded linear operators, M. Dekker, 1987. Zbl0636.47001MR920812
  64. HEINRICH, S., Finite representability of operators, Proc. Int. Conf. operators algebras, ideals and applications, Leipzig (1977), 33-39. Zbl0405.47028MR528256
  65. HEINRICH, S., Ultraproducts in Banach space Theory, J. Reine Angew. Math., 313 (1980), 72-104. Zbl0412.46017MR552464
  66. HEINRICH, S., Closed operator ideals and interpolation, J. Funct. Anal., 35 (1980), 397-411. Zbl0439.47029MR563562
  67. HERMAN, R. H., Generalizations of weakly compact operators, Trans. Amer. Math. Soc., 132 (1968), 377-386. Zbl0159.43004MR223929
  68. HOLUB, J. R., Characterizations of tauberian and related operators on Banach spaces, J. Math. Anal. Appl., 178 (1993), 280-288. Zbl0804.47002MR1231742
  69. KALTON, N.- WILANSKY, A., Tauberian operators in Banach spaces, Proc. Amer. Math. Soc., 57 (1976), 251-255. Zbl0304.47023MR473896
  70. KLEINECKE, D., Almost-finite, compact, and inessential operators, Proc. Amer. Math. Soc., 14 (1963), 863-868. Zbl0117.34201MR155197
  71. LEBOW, A.- SCHECHTER, M., Semigroups of operators and measures of noncompactness, J. Funct. Anal., 7 (1971), 1-26. Zbl0209.45002MR273422
  72. LINDENSTRAUSS, J.- TZAFRIRI, L., Classical Banach Spaces I. Sequence spaces, Springer-Verlag, Berlin, Heidelberg, New York, 1977. Zbl0362.46013MR500056
  73. LOHMAN, R., A note on Banach spaces containing l 1 , Canad. Math. Bull., 19 (1976), 365-367. Zbl0342.46006MR430748
  74. LOTZ, H.- PECK, N.- PORTA, H., Semi-embeddings of Banach spaces, Proc. Edinburgh Math. Soc., 12 (1979), 233-240. Zbl0405.46013MR560985
  75. MARTIN, D. H.- SWART, J., A characterisation of semi-Fredholm operators defined on an almost-reflexive normed spaces, Proc. R. Ir. Acad. A, 86 (1986), 91-93. Zbl0587.47015MR865107
  76. MARTÍNEZ-ABEJÓN, A., Semigrupos de operadores y ultrapotencias, Ph. D. Thesis Univ. Cantabria, 1994. 
  77. MARTÍNEZ-MAURICA, J.- PELLÓN, T., Non-archimedian tauberian operators, Proc. Conf. on p -adic analysis Hengelhoef (1986), 101-111. Zbl0628.46078MR921862
  78. MARTINÓN, A., Cantidades operacionales en teoria de Fredholm, Ph. D. Thesis Univ. La Laguna, 1989. MR1067932
  79. NEIDINGER, R., Properties of tauberian operators in Banach spaces, Ph. D. Thesis Univ. Texas at Austin, 1984. 
  80. NEIDINGER, R.- ROSENTHAL, H. P., Norm-attainment of linear functionals on subspaces and characterizations of tauberian operators, Pacific J. Math., 118 (1985), 215-228. Zbl0537.46018MR783025
  81. PIETSCH, A., Inessential operators in Banach spaces, Integral Equations and Operator Theory, 1 (1978), 589-591. Zbl0399.47040MR516770
  82. PIETSCH, A., Operator ideals, North-Holland, Amsterdam, New York, Oxford, 1980. Zbl0434.47030MR582655
  83. ROSENTHAL, H. P., On totally incomparable Banach spaces, J. Funct. Anal., 4 (1969), 167-175. Zbl0184.15004MR248506
  84. ROSENTHAL, H. P., On wide- s sequences and their applications to certain classes of operators, Pacific J. Math., 189 (1999), 311-338. Zbl0932.46007MR1696126
  85. SCHACHERMAYER, W., For a Banach space isomorphic to its square the Radon-Nikodym property and the Krein-Milman property are equivalent, Studia Math., 81 (1985), 329-339. Zbl0631.46019MR808576
  86. SCHECHTER, M., Quantities related to strictly singular operators, Indiana Univ. Math. J., 21 (1972), 1061-1071. Zbl0274.47007MR295103
  87. TACON, D. G., Generalized semi-Fredholm transformations, J. Austral. Math. Soc. A, 34 (1983), 60-70. Zbl0531.47011MR683179
  88. TACON, D. G., Generalized Fredholm transformations, J. Austral. Math. Soc. A, 37 (1984), 89-97. Zbl0605.47010MR742246
  89. TALAGRAND, M., The three-space problem for L 1 , J. Amer. Math. Soc., 3 (1990), 9-29. Zbl0727.46012MR1013926
  90. TARAFDAR, E., On further properties of improjective operators, J. Austral. Math. Soc., 14 (1972), 352-363. Zbl0251.47037MR315497
  91. TAYLOR, A. E.- LAY, D. C., Introduction to functional analysis, 2nd ed., Wiley, 1980. Zbl0501.46003MR564653
  92. TYLLI, H.-O., Two approximation conditions relative to closed operator ideals, Preprint, 1990. 
  93. WEIS, L., On perturbations of Fredholm operators in L p μ -spaces, Proc. Amer. Math. Soc., 67 (1977), 287-292. Zbl0377.46016MR467377
  94. WEIS, L., Perturbation classes of semi-Fredholm operators, Math. Z., 178 (1981), 429-442. Zbl0541.47010MR635212
  95. WHITLEY, R. J., Strictly singular operators and their conjugates, Trans. Amer. Math. Soc., 113 (1964), 252-261. Zbl0124.06603MR177302
  96. YANG, K. W., The generalized Fredholm operators, Trans. Amer. Math. Soc., 216 (1976), 313-326. Zbl0297.47027MR423114
  97. YANG, K. W., Operator invertible modulo the weakly compact operators, Pacific J. Math., 71 (1977), 559-564. Zbl0359.47019MR461193
  98. ZEMANEK, J., Geometric characteristics of semi-Fredholm operators and their asymptotic behaviour, Studia Math., 80 (1984), 219-234. Zbl0556.47008MR783991

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