Banach spaces with the differentiable norms

Václav Zizler

Commentationes Mathematicae Universitatis Carolinae (1968)

  • Volume: 009, Issue: 3, page 415-440
  • ISSN: 0010-2628

How to cite

top

Zizler, Václav. "Banach spaces with the differentiable norms." Commentationes Mathematicae Universitatis Carolinae 009.3 (1968): 415-440. <http://eudml.org/doc/16287>.

@article{Zizler1968,
author = {Zizler, Václav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {functional analysis},
language = {eng},
number = {3},
pages = {415-440},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Banach spaces with the differentiable norms},
url = {http://eudml.org/doc/16287},
volume = {009},
year = {1968},
}

TY - JOUR
AU - Zizler, Václav
TI - Banach spaces with the differentiable norms
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1968
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 009
IS - 3
SP - 415
EP - 440
LA - eng
KW - functional analysis
UR - http://eudml.org/doc/16287
ER -

References

top
  1. N. I. ACHIJEZER M. G. KREJN, O nekotorych voprosach teorii momentov, Charkov 1938. (1938) 
  2. Edgar ASPLUND, Averaged norms, Israel Journal of Mathem. 5 (1967), 4, 227-233. (1967) MR0222610
  3. Edgar ASPLUND, Positivity of duality mappings, Bull. of the Amer. Math. Soc. 73, 2, 200-204. MR0206663
  4. S. BANACH, Théoriedes operations linéaires, Warsaw, 1932. (1932) 
  5. A. BECK, A convexity condition in Banach spaces and the strong law of large numbers, PANS 13 (1962), 329-334. (1962) Zbl0108.31401MR0133857
  6. E. BISHOP R. R. PHELPS, A proof that every Banach - space is subreflexive, Bull. of the Amer. Math. Soc. 67, 79-98. MR0123174
  7. C. BESSAGA A. PELCZYŃSKI, Some remarks on homeomorphism of Banach spaces, Bull. de L. Acad. Pol. VIII, N. 11-12 (1960), 757-761. (1960) MR0132385
  8. C. BESSAGA A. PELCZYŃSKI, On extreme points in separable conjugate spaces, Israel Journal of Mathem. 4 (1966), 262-264. (1966) MR0211244
  9. C. BESSAGA, Topological equivalence of nonseparable reflexive Banach spaces, Bull. de L. Acad. Pol. 15 (1967), No. 6, 397-399. (1967) MR0221269
  10. H. BONIC J. FRAMPTON, Smooth functions on Banach manifolds, Journal of Math. and Mech. 15 (1966), No 5, 877-898. (1966) MR0198492
  11. R. BONIC F. REIS, A characterization of Hilbert space, Anais da Academia Brasileira de Cienc. 38 (1966) No 2, 239-241. (1966) MR0218877
  12. A. BEURLING A. E. LIVINGSTON, A theorem on duality mappings in Banach spaces, Ark. for Mat. 4 (1960-1963), 405-411. (1960) MR0145320
  13. M. S. BRODSKIJ D. P. MILMAN, O centre vypuklogo množestva, Dokl. Ak. Nauk SSSR 59, 837-840. 
  14. F. E. BROWDER, Nonexpansive nonlinear operators in Banach spaces, Proc. of the Nat. Ac. Sc. USA 54 (1965), 4, 1041-1044. (1965) MR0187120
  15. F. E. BROWDER, On a theorem of Beurling and Livingston, Canad. J. Math. 17 (1965), 367-372. (1965) MR0176320
  16. F. E. BROWDER D. G. FIGUEIREDO, J-monotone nonlinear operators in Banach spaces, Konkl. Nederl. Akad. Weten. 69 (1966), 412-420. (1966) MR0205122
  17. J. A. CLARKSON, Uniformly convex spaces, Trans. of the Amer. Math. Soc. 40 (1936), 396-414. (1936) Zbl0015.35604MR1501880
  18. D. F. CUDIA, The geometry of Banach spaces, Smoothness, Trans. of the Amer. Math. Soc. 110 (1964), 284-314. (1964) Zbl0123.30701MR0163143
  19. D. F. CUDIA, Rotundity, Proc. of Symposia in Pure Math. Vol. VII, 1963, 73-97. (1963) Zbl0141.11901MR0155166
  20. J. DANEŠ, Some fixed point theorems, Comment. Math. Univ. Carol. 9, 2 (1968), 223-235. (1968) MR0235435
  21. J. DANEŠ, Continuity properties of nonlinear mappings, Comment. Math. Univ. Carol. 9, 3 (1968) (this volume). (1968) MR0236779
  22. M. M. DAY, Reflexive Banach spaces not isomorphic to uniformly convex spaces, Bull. of the Amer. Math. Soc. 47 (1941), 313-317. (1941) Zbl0024.41401MR0003446
  23. M. M. DAY, Some more uniformly convex spaces, Bull. of the Amer. Math. Soc. 47, 504-517. Zbl0027.11003MR0004068
  24. M. M. DAY, Uniform convexity III, Bull. of the Amer. Math. Soc. 49 (1943), 745-150. (1943) Zbl0063.01056MR0009422
  25. M. M. DAY, Uniform convexity in factor and conjugate spaces, Ann. of Math. 45 (1944), 375-385. (1944) Zbl0063.01058MR0010779
  26. M. M. DAY, Strict convexity and smoothness of normed spaces, Trans. of the Amer. Math. Soc. 78 (1955), 516-528. (1955) Zbl0068.09101MR0067351
  27. M. M. DAY, Normed linear spaces, (russian translation Moscow 1961). (1961) Zbl0098.30401MR0121626
  28. N. DUNFORD J. T. SCHWARTZ, Linear operators I, (russian translation), Moscov 1962. (1962) MR0216303
  29. J. DIEUDONNÉ, Foundations of modern analysis, (russian translation, Moscow 1964). (1964) 
  30. K. FAN I. GLICKSBERG, Fully convex normed linear spaces, Proc. of the Nat. Ac. Sc. USA 41 (1955), 947-953. (1955) MR0073120
  31. K. FAN I. GLICKSBERG, Some geometric properties of the spheres in a normed linear space, Duke Math. Journ. 25, 553-567. MR0098976
  32. D. G. FIGUEIREDO, Topics in nonlinear functional analysis, Lecture Series, N. 48, University of Maryland 1967. (1967) 
  33. M. FRÉCHET, Sur la notion de différentielle, Journal de Math. 16 (1937), 233-250. (1937) 
  34. D. P. GIESY, A convexity condition on Banach spaces invariant under conjugation, Amer. Math. Soc. Notices 10 (1963), p. 665, abstract 607-15. (1963) 
  35. G. GODINI, On the localization and directionalization of uniform convexity and uniform emoothness, Rev. Roum. de Math. Pur. et Appl. T XI, N. 10 (1966), 1233-1240. (1966) MR0217565
  36. D. GÖHDE, Zum Prinzip der kontraktiven Abbildung, Mat. Nach. 30 (1965), 251-258. (1965) MR0190718
  37. V. I. GURARIJ, O ravnomerno vypuklych i ravnomerno gladkich Banachovych prostranstvach, Teorija funkcij, funkc. anal. i ich pril. 1 (1965), 205-211. (1965) 
  38. V. I. GURARIJ, O moduljach vypuklosti i gladkosti Banachovych prostranstv, Dokl. Ak. Nauk SSSR 6, 535-539. 
  39. E. HILLE R. S. PHILLIPS, Functional analysis and semigroups, (russian translation, Moscow 1962). (1962) 
  40. N. A. IVANOV, O differencialach Gato i Freše, Uspechi mat. nauk SSSR 10 (1955), 2, 161-166. (1955) 
  41. R. C. JAMES, Reflexivity and supremum of linear functionals, Ann. of Math. 1957, 66, 159-169. (1957) MR0090019
  42. R. C. JAMES, Characterization of reflexivity, Studia Math. XXIII (1964), 205-216. (1964) MR0170192
  43. R. C. JAMES, Weak compactness and reflexivity, Israel Journal of Mathem. 2 (1964), 101-119. (1964) Zbl0127.32502MR0176310
  44. R. C. JAMES, Uniformly non-squared Banach spaces, Ann. of Math. 80 (1964), 542-550. (1964) MR0173932
  45. R. C. JAMES, Bases and reflexivity of Banach spaces, Ann. of Math. 52 (1950), 518-527. (1950) Zbl0039.12202MR0039915
  46. N. N. JEFIMOV S. B. STEČKIN, Nekotoryje svojstva Čebyševskich množestv, Dokl. Ak. Nauk SSSR 118, 1, p. 17-19. 
  47. N. N. JEFIMOV S. B. STEČKIN, Čebyševskije množestva v prostranstvach Banacha, Dokl. Ak. Nauk SSSR 121, 582-585. 
  48. N. N. JEFIMOV S. B. STEČKIN, Opornyje svojstva množestv v Banachovych prostranstvach i Čebyševskije množestva, Dokl. Ak. Nauk SSSR 127, 254-257. 
  49. M. I. KADEC, Pro zvjazok miž slaboju ta silnoju zbižnistju, Dopovidi Akad. Nauk Ukrain. RSR 9 (1959), 949-951. (1959) 
  50. M. I. KADEC, O gomeomorfismach nekotorych prostranstv Banacha, Dokl. Ak. Nauk SSSR, T XCII (1953), p. 465-468. (1953) MR0059469
  51. M. I. KADEC, O slaboj i silnoj schodimosti, Dokl. Ak. Nauk SSSR 122 (1958), No 1, p. 13. (1958) MR0098977
  52. M. I. KADEC, Topologičeskaja ekvivalentnosť vsech separabelnych prostranstv Banacha, Dokl. Ak. Nauk SSSR 167 (1966), N. 1, 23-25. (1966) MR0201951
  53. M. I. KADEC, O topologičeskoj ekvivalentnosti ravnomerno vypuklych prostranstv, Uspechi mat. nauk SSSR 10, 4 (1955), 137-142. (1955) MR0073939
  54. M. I. KADEC, O prostranstvach isomorfnych lokalno ravnomerno vypuklyn prostranstvam, Izv. vyšš. uč. zav. Matem: 1 (8) (1959), No 6, 51-57 and 1 (20) (1961), No. 6, 186-187. (1959) 
  55. M. I. KADEC, Uslovija differencirujemosti normy Banachova prostranstva, Uspechi mat. nauk SSSR T XX, 3 (123), 183-187. MR0185416
  56. S. KAKUTANI, Weak convergence in uniformly convex spaces, Tohoku Math. Journ. 45 (1939), 188-193. (1939) 
  57. T. KATO, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan, Vol. 19 (1967), 508-520. (1967) Zbl0163.38303MR0226230
  58. W. A. KIRK, A fixed point theorem for mappings which do not increase distance, Amer. Math. Monthly 72 (1965), 1004-1006. (1965) MR0189009
  59. V. L. KLEE, Some characterizations of reflexivity, Revista Ci. Lima, 12 (1950), 15-23. (1950) Zbl0040.35403MR0043364
  60. V. L. KLEE, Convex bodies and periodic homeomorphisms in Hilbert spaces, Trans. of the Amer. Math. Soc. 74 (1953), 10-43. (1953) MR0054850
  61. V. L. KLEE, Extremal structure of convex sets II, Math. Zeit. 69 (1958), 90-104. (1958) Zbl0079.12502MR0092113
  62. V. L. KLEE, Mappings into normed linear spaces, Fundamenta Math. 49 (1960-61), 25-34. (1960) Zbl0117.08303MR0126690
  63. V. L. KLEE, Some new results on smoothness and rotundity in normed linear spaces, Math. Ann. 139, 51-63. Zbl0092.11602MR0115076
  64. V. L. KLEE, Convexity of Chebyshev sets, Math. Ann. 142, 292-304. Zbl0091.27701
  65. J. KOLOMÝ, On the differentiability of mappings in functional spaces, Comment. Math. Univ. Carol. 8, 2 (1967), 315-331. (1967) MR0212569
  66. J. KOLOMÝ, On the differentiability of mappings and convex functional, Comment. Math. Univ. Carol. 8, 4 (1967), 735-753. (1967) MR0243348
  67. J. KOLOMÝ, On the differentiability of mappings and convex functionals, Comment. Math. Univ. Carol. 8, 4 (1967), 735-752 (see also Comment. Math. Univ. Carol. 9, 1 (1968), p. 1971). (1967) MR0243348
  68. J. DANEŠ J. KOLOMÝ, On the continuity and differentiability of convex functionals, Comment. Math. Univ. Carol. 9, 2 (1968), 329-350. (1968) MR0239415
  69. J. KOLOMÝ V. ZIZLER, Remarks on the differentiability of mappings in linear normed spaces, Comment. Math. Univ. Carol. 8, 4 (1967), 691-705. (1967) MR0234279
  70. G. KÖTHE, Topologische lineare Räume, Berlin 1960. (1960) 
  71. J. KURZWEIL, On approximation in real Banach spaces, Studia Math. 14, 214-231. Zbl0080.32602MR0068732
  72. J. KURZWEIL, A characterization of analytic operations in real Banach spaces, Studia Math. 14 (1953), 82-83. (1953) Zbl0052.34602MR0062948
  73. S. LANG, Introduction to differentiable manifolds, New York 1962 (russian translation). (1962) Zbl0103.15101MR0155257
  74. J. LINDENSTRAUSS, On the modulus of smoothness and divergent series in Banach spaces, Michigan Math. J. 10 (1963), 241-252. (1963) Zbl0115.10001MR0169061
  75. J. LINDENSTRAUSS, On operators which attain their norm, Israel Journal of Mathem. 1 (1963), 139-148. (1963) Zbl0127.06704MR0160094
  76. J. LINDENSTRAUSS, On reflexive spaces having the metric approximation property, Israel Journal of Mathem. 3 (1965), 199-204. (1965) Zbl0148.11302MR0205039
  77. J. LINDENSTRAUSS, On nonseparable reflexive Banach spaces, Bull. of the Amer. Math. Soc. 1966, 967-970. (1966) Zbl0156.36403MR0205040
  78. J. LINDENSTRAUSS, On complemented subspace of m , Israel Journal of Mathem. 5 (1967), 153-156. (1967) MR0222616
  79. J. LINDENSTRAUSS, On extrene points in l 1 , Israel Journal of Mathem. 4 (1966), 59-61. (1966) MR0200701
  80. J. LINDENSTRAUSS R. R. PHELPS, Extreme point properties of convex bodies in reflexive Banach spaces, Israel Journal of Mathem. 6, 1 (1968), 39-48. (1968) MR0234260
  81. A. R. LOVAGLIA, Locally uniformly convex Banach spaces, Trans. of the Amer. Math. Soc. 78 (1958), 225-238. (1958) MR0066558
  82. G. MARINESCU, Asupra diferentialei si derivatei in spatiile normate, Bull. Stiint. Acad. R. P. Romine Sec. mat. si fiz. 6 (1954), N. 2, 213-219. (1954) 
  83. S. MAZUR, Über konvexe Mengen in linearen normierten Räumen, Studia Math. 4 (1933), 70-84. (1933) Zbl0008.31603
  84. S. MAZUR, Über schwache Konvergenz in den Räumen L p , Studia Math. 4 (1933), 128-133. (1933) 
  85. D. MILMAN, On some criteria for the regularity of spaces of the type (B), C. R. Acad. Sci. USSR 20 (1938), 243-246. (1938) Zbl0019.41601
  86. I. NAMIOKA, Neighbourhoods of extreme points, Israel Journal of Mathem. 1967, N. 3, 145-152. (1967) MR0221271
  87. J. RAINWATER, Weak convergence of bounded sequences, Proc. of the Amer. Math. Soc. 1963, p. 999. (1963) Zbl0117.08302MR0155171
  88. M. M. RAO, Characterizing Hilbert space by smoothness, Reprinted from Proceedings. Series A, Vol. LXX, No. 1 (1967), 132-135. (1967) Zbl0145.16201MR0211249
  89. G. RESTREPO, Differentiable norms in Banach spaces, Bull. of the Amer. Math. Soc. 70 (1964), 413-414. (1964) MR0161129
  90. I. SINGER, On Banach spaces reflexive with respect to a linear subspace of their conjugate space, Bull. Math. de la Soc. Sci. Math. Phys. de R. P. R. n. Sér. 2 (50), No 4 (1958), 449-462. (1958) Zbl0098.08001MR0117530
  91. G. A. SUCHOMLINOV, Analitičeskije funkcionaly, Bjull. Moskov. univ. sekcija A, T 1 (1937), 1-19. (1937) 
  92. R. SUNDARESAN, Smooth Banach spaces, Math. Ann. 173 (1967), Heft 3, 191-199. (1967) Zbl0158.13701MR0218876
  93. V. L. ŠMULJAN, O nekotorych geometričeskich svojstvach sfery v prostranstvach tipa B, Dokl. Ak. Nauk SSSR 24 (1939), 647-651. (1939) 
  94. V. L. ŠMULJAN, O principu vkladok v prostranstve tipa B, Matem. Sb. 5 (47) (1939), 317-328. (1939) 
  95. V. L. ŠMULJAN, O nekotorych geometričeskich svojstvach jediničnoj sfery prostranstva tipa B, Matem. Sb. 6 (48) (1939), 77-94. (1939) 
  96. V. L. ŠMULJAN, O differencirujemosti normy v prostranstve Banacha, Dokl. Ak. Nauk SSSR 27 (1940), 643-648. (1940) 
  97. V. L. ŠMULJAN, Sur la structure de la sphere unitaire dans l'espace de Banach, Matem. Sbornik 9 (1941), 545-572. (1941) 
  98. S. TROJANSKIJ, Topologičeskaja ekvivalentnosť prostranstv C 0 ( λ ) , l 1 ( λ ) , Bull. de L. Acad. Pol. XV, 6 (1967), 389-396. (1967) 
  99. M. M. VAJNBERG, Variacionnyje metody issledovanija nelinejnych operatorov, Moskva 1956. (1956) 
  100. L. P. VLASOV, O Čebyševskich množstvach, Dokl. Ak. Nauk SSSR 173 (1967), 491-494. (1967) MR0215059
  101. L. P. VLASOV, Approximativno vypuklyje množestva v Banachovych prostranstvach, Dokl. Ak. Nauk SSSR 163 (1965), 18-21. (1965) 
  102. L. P. VLASOV, O Čebyševskich množestvach v Banachovych prostranstvach, Dokl. Ak. Nauk SSSR 141, 19-20. 
  103. L. P. VLASOV, Approximativno vypuklyje množestva v ravnomerno gladkich prostranstvach, Matem. Zametki 1 (1967), 443-450. (1967) 
  104. J. WADA, Strict convexity and smoothness of normed spaces, Osaka J. Math. 10 (1958), 221-230. (1958) Zbl0084.09804MR0100775
  105. K. YOSHIDA, Functional analysis, (russian translation Moscow 1967). (1967) 
  106. V. ZIZLER, On tne differentiability of mappings in Banach spaces, Comment. Math. Univ. Carol. 8, 3 (1967), 415-430. (1967) MR0227772

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.