Some notes on various rotundity and smoothness properties of separable Banach spaces

Václav Zizler

Commentationes Mathematicae Universitatis Carolinae (1969)

  • Volume: 010, Issue: 2, page 195-206
  • ISSN: 0010-2628

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Zizler, Václav. "Some notes on various rotundity and smoothness properties of separable Banach spaces." Commentationes Mathematicae Universitatis Carolinae 010.2 (1969): 195-206. <http://eudml.org/doc/16320>.

@article{Zizler1969,
author = {Zizler, Václav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {functional analysis},
language = {eng},
number = {2},
pages = {195-206},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Some notes on various rotundity and smoothness properties of separable Banach spaces},
url = {http://eudml.org/doc/16320},
volume = {010},
year = {1969},
}

TY - JOUR
AU - Zizler, Václav
TI - Some notes on various rotundity and smoothness properties of separable Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1969
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 010
IS - 2
SP - 195
EP - 206
LA - eng
KW - functional analysis
UR - http://eudml.org/doc/16320
ER -

References

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  1. E. ASPLUND, Averaged noms, Israel Journ. of Math. 5 (1967), 4, 227-233. (1967) MR0222610
  2. S. BANACH, Théorie des opérations linéaires, Warsaw, 1932. (1932) Zbl0005.20901
  3. M. S. BRODSKIJ D. P. MILMAN, O centre vypuklogo množestva, Dokl. Ak. Nauk SSSR 59 (1948), 837-840. (1948) MR0024073
  4. A. BRØNDSTED, Conjugate convex functions in topological vector spaces, Mat. - Fys. Medd. Dansk. Vid. Selsk. 34 (1964), 2. (1964) MR0166580
  5. D. F. CUDIA, Rotundity, Proceedings of Symp. in Pure Math., VII, 1963, 73-97. (1963) Zbl0141.11901MR0155166
  6. D. F. CUDIA, The geometry of Banach spaces. Smoothness, Trans. of the Am. Math. Soc. 110 (1964), 284-314. (1964) Zbl0123.30701MR0163143
  7. M. M. DAY, Reflexive Banach spaces not isomorphic to uniformly convex spaces, Bull. Am. Math. Soc. 47 (1941), 313-317. (1941) Zbl0024.41401MR0003446
  8. M. M. DAY, Strict convexity and smoothness of normed spaces, Trans. of Am. Math. Soc. 78 (1955), 516-528. (1955) Zbl0068.09101MR0067351
  9. M. M. DAY, Normed linear spaces, Ergeb. Math. Gr. (N. F.) no. 21, Springer, Berlin 1958, Russian translation, Moscow 1961. (1958) Zbl0082.10603MR0094675
  10. M. I. KADEC, O prostranstvech izomorfnych lokalno ravnomerno vypuklym prostranstvam, Izv. vysš. uč. zav. Matem. 1 (8) (1959), No. 6, 51-57 and 1 (20) (1961), 6, 186-187. (1959) MR0126692
  11. M. I. KADEC, Uslovija differencirujemosti normy Banachova prostranstva, Uspechi Matem. nauk T XX, 3, 123, 183-187. 
  12. M. I. KADEC, Oslaboj i silnoj schodimosti, Dokl. Ak. Nauk SSSR 122 (1958), 13-16. (1958) 
  13. V. L. KLEE, Mappings into normed linear spaces, Fundamenta Math. XLIX (1960), 25-34. (1960) Zbl0117.08303MR0126690
  14. V. L. KLEE, Convex bodies and periodic homeomorphisms in Hilbert space, Trans. Am. Math. Soc. 74 (1953), 10-43. (1953) Zbl0050.33202MR0054850
  15. V. L. KLEE, Some new results on smoothness and rotundity in normed linear spaces, Math. Ann. 139 (1959), 51-63. (1959) Zbl0092.11602MR0115076
  16. A. R. LOVAGLIA, Locally uniformly convex Banach spaces, Trans. of Am. Math. Soc. 78 (1955), 225-238. (1955) Zbl0064.35601MR0066558
  17. G. RESTREPO, Differentiable norms in Banach spaces, Bull. Am. Math. Soc. 70 (1964), 413-414. (1964) MR0161129
  18. V. L. ŠMULJAN, On some geometrical properties of the unit sphere in the space of the type (B), Mat. Sb. (N. S.) 6 (48) (1939), 77-94. (1939) MR0001458
  19. V. L. ŠMULJAN, Sur la dérivabilité de la norme dans l'espace de Banach, Dokl. Ak. Nauk SSSR (N. S.) 27 (1940), 643-648. (1940) MR0002704
  20. V. L. ŠMULJAN, O nekotorych geometričeskich svojstvach sfery v prostranstvach tipa B, Dokl. Ak. Nauk SSSR 24 (1939), 647-651. (1939) 
  21. V. L. ŠMULJAN, Sur la strucrture de la sphère unitaire dans l'espace de Banach, Mat. Sb. 9 (1941), 545-572. (1941) 
  22. R. VÝBORNÝ, O slabé konvergenci v prostorech lokálně stejnoměrně konvexních, Časopis pro pěstování matem. (ČSSR) 81 (1956), 352-353. (1956) 
  23. V. ZIZLER, Banach spaces with the differentiable norms, Comment. Math. Univ. Carolinae 9, 3 (1968), 415-440. (1968) Zbl0182.45105MR0246121
  24. V. ZIZLER, One theorem on rotundity and smoothness of separable Banach spaces, Comment. Math. Univ. Carolinae 9, 4 (1968), 637-640. (1968) MR0256139

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