Title:
|
Banach spaces with the differentiable norms (English) |
Author:
|
Zizler, Václav E. |
Language:
|
English |
Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
ISSN:
|
0010-2628 (print) |
ISSN:
|
1213-7243 (online) |
Volume:
|
9 |
Issue:
|
3 |
Year:
|
1968 |
Pages:
|
415-440 |
. |
Category:
|
math |
. |
MSC:
|
46-45 |
MSC:
|
46Bxx |
idZBL:
|
Zbl 0182.45105 |
idMR:
|
MR0246121 |
. |
Date available:
|
2008-06-05T20:28:36Z |
Last updated:
|
2012-04-27 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/105190 |
. |
Reference:
|
[1] N. I. ACHIJEZER M. G. KREJN: O nekotorych voprosach teorii momentov.Charkov 1938. |
Reference:
|
[1a] Edgar ASPLUND: Averaged norms.Israel Journal of Mathem. 5 (1967), 4, 227-233. MR 0222610 |
Reference:
|
[2] Edgar ASPLUND: Positivity of duality mappings.Bull. of the Amer. Math. Soc. 73, 2, 200-204. MR 0206663 |
Reference:
|
[3] S. BANACH: Théoriedes operations linéaires.Warsaw, 1932. |
Reference:
|
[4] A. BECK: A convexity condition in Banach spaces and the strong law of large numbers.PANS 13 (1962), 329-334. Zbl 0108.31401, MR 0133857 |
Reference:
|
[5] E. BISHOP R. R. PHELPS: A proof that every Banach - space is subreflexive.Bull. of the Amer. Math. Soc. 67, 79-98. MR 0123174 |
Reference:
|
[6] C. BESSAGA A. PELCZYŃSKI: Some remarks on homeomorphism of Banach spaces.Bull. de L. Acad. Pol. VIII, N. 11-12 (1960), 757-761. MR 0132385 |
Reference:
|
[7] C. BESSAGA A. PELCZYŃSKI: On extreme points in separable conjugate spaces.Israel Journal of Mathem. 4 (1966), 262-264. MR 0211244 |
Reference:
|
[8] C. BESSAGA: Topological equivalence of nonseparable reflexive Banach spaces.Bull. de L. Acad. Pol. 15 (1967), No. 6, 397-399. MR 0221269 |
Reference:
|
[9] H. BONIC J. FRAMPTON: Smooth functions on Banach manifolds.Journal of Math. and Mech. 15 (1966), No 5, 877-898. MR 0198492 |
Reference:
|
[10] R. BONIC F. REIS: A characterization of Hilbert space.Anais da Academia Brasileira de Cienc. 38 (1966) No 2, 239-241. MR 0218877 |
Reference:
|
[11] A. BEURLING A. E. LIVINGSTON: A theorem on duality mappings in Banach spaces.Ark. for Mat. 4 (1960-1963), 405-411. MR 0145320 |
Reference:
|
[12] M. S. BRODSKIJ D. P. MILMAN: O centre vypuklogo množestva.Dokl. Ak. Nauk SSSR 59, 837-840. |
Reference:
|
[13] F. E. BROWDER: Nonexpansive nonlinear operators in Banach spaces.Proc. of the Nat. Ac. Sc. USA 54 (1965), 4, 1041-1044. MR 0187120 |
Reference:
|
[14] F. E. BROWDER: On a theorem of Beurling and Livingston.Canad. J. Math. 17 (1965), 367-372. MR 0176320 |
Reference:
|
[15] F. E. BROWDER D. G. FIGUEIREDO: J-monotone nonlinear operators in Banach spaces.Konkl. Nederl. Akad. Weten. 69 (1966), 412-420. MR 0205122 |
Reference:
|
[16] J. A. CLARKSON: Uniformly convex spaces.Trans. of the Amer. Math. Soc. 40 (1936), 396-414. Zbl 0015.35604, MR 1501880 |
Reference:
|
[17] D. F. CUDIA: The geometry of Banach spaces.Smoothness, Trans. of the Amer. Math. Soc. 110 (1964), 284-314. Zbl 0123.30701, MR 0163143 |
Reference:
|
[18] D. F. CUDIA: Rotundity.Proc. of Symposia in Pure Math. Vol. VII, 1963, 73-97. Zbl 0141.11901, MR 0155166 |
Reference:
|
[19] J. DANEŠ: Some fixed point theorems.Comment. Math. Univ. Carol. 9, 2 (1968), 223-235. MR 0235435 |
Reference:
|
[20] J. DANEŠ: Continuity properties of nonlinear mappings.Comment. Math. Univ. Carol. 9, 3 (1968) (this volume). MR 0236779 |
Reference:
|
[21] M. M. DAY: Reflexive Banach spaces not isomorphic to uniformly convex spaces.Bull. of the Amer. Math. Soc. 47 (1941), 313-317. Zbl 0024.41401, MR 0003446 |
Reference:
|
[22] M. M. DAY: Some more uniformly convex spaces.Bull. of the Amer. Math. Soc. 47, 504-517. Zbl 0027.11003, MR 0004068 |
Reference:
|
[23] M. M. DAY: Uniform convexity III.Bull. of the Amer. Math. Soc. 49 (1943), 745-150. Zbl 0063.01056, MR 0009422 |
Reference:
|
[24] M. M. DAY: Uniform convexity in factor and conjugate spaces.Ann. of Math. 45 (1944), 375-385. Zbl 0063.01058, MR 0010779 |
Reference:
|
[25] M. M. DAY: Strict convexity and smoothness of normed spaces.Trans. of the Amer. Math. Soc. 78 (1955), 516-528. Zbl 0068.09101, MR 0067351 |
Reference:
|
[26] M. M. DAY: Normed linear spaces.(russian translation Moscow 1961). Zbl 0098.30401, MR 0121626 |
Reference:
|
[27] N. DUNFORD J. T. SCHWARTZ: Linear operators I.(russian translation), Moscov 1962. MR 0216303 |
Reference:
|
[28] J. DIEUDONNÉ: Foundations of modern analysis.(russian translation, Moscow 1964). |
Reference:
|
[29] K. FAN I. GLICKSBERG: Fully convex normed linear spaces.Proc. of the Nat. Ac. Sc. USA 41 (1955), 947-953. MR 0073120 |
Reference:
|
[30] K. FAN I. GLICKSBERG: Some geometric properties of the spheres in a normed linear space.Duke Math. Journ. 25, 553-567. MR 0098976 |
Reference:
|
[31] D. G. FIGUEIREDO: Topics in nonlinear functional analysis.Lecture Series, N. 48, University of Maryland 1967. |
Reference:
|
[32] M. FRÉCHET: Sur la notion de différentielle.Journal de Math. 16 (1937), 233-250. |
Reference:
|
[33] D. P. GIESY: A convexity condition on Banach spaces invariant under conjugation.Amer. Math. Soc. Notices 10 (1963), p. 665, abstract 607-15. |
Reference:
|
[34] 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. MR 0217565 |
Reference:
|
[35] D. GÖHDE: Zum Prinzip der kontraktiven Abbildung.Mat. Nach. 30 (1965), 251-258. MR 0190718 |
Reference:
|
[36] V. I. GURARIJ: O ravnomerno vypuklych i ravnomerno gladkich Banachovych prostranstvach.Teorija funkcij, funkc. anal. i ich pril. 1 (1965), 205-211. |
Reference:
|
[37] V. I. GURARIJ: O moduljach vypuklosti i gladkosti Banachovych prostranstv.Dokl. Ak. Nauk SSSR 6, 535-539. |
Reference:
|
[38] E. HILLE R. S. PHILLIPS: Functional analysis and semigroups.(russian translation, Moscow 1962). |
Reference:
|
[39] N. A. IVANOV: O differencialach Gato i Freše.Uspechi mat. nauk SSSR 10 (1955), 2, 161-166. |
Reference:
|
[40] R. C. JAMES: Reflexivity and supremum of linear functionals.Ann. of Math. 1957, 66, 159-169. MR 0090019 |
Reference:
|
[41] R. C. JAMES: Characterization of reflexivity.Studia Math. XXIII (1964), 205-216. MR 0170192 |
Reference:
|
[42] R. C. JAMES: Weak compactness and reflexivity.Israel Journal of Mathem. 2 (1964), 101-119. Zbl 0127.32502, MR 0176310 |
Reference:
|
[43] R. C. JAMES: Uniformly non-squared Banach spaces.Ann. of Math. 80 (1964), 542-550. MR 0173932 |
Reference:
|
[44] R. C. JAMES: Bases and reflexivity of Banach spaces.Ann. of Math. 52 (1950), 518-527. Zbl 0039.12202, MR 0039915 |
Reference:
|
[44a] N. N. JEFIMOV S. B. STEČKIN: Nekotoryje svojstva Čebyševskich množestv.Dokl. Ak. Nauk SSSR 118, 1, p. 17-19. |
Reference:
|
[44b] N. N. JEFIMOV S. B. STEČKIN: Čebyševskije množestva v prostranstvach Banacha.Dokl. Ak. Nauk SSSR 121, 582-585. |
Reference:
|
[44c] N. N. JEFIMOV S. B. STEČKIN: Opornyje svojstva množestv v Banachovych prostranstvach i Čebyševskije množestva.Dokl. Ak. Nauk SSSR 127, 254-257. |
Reference:
|
[45] M. I. KADEC: Pro zvjazok miž slaboju ta silnoju zbižnistju.Dopovidi Akad. Nauk Ukrain. RSR 9 (1959), 949-951. |
Reference:
|
[46] M. I. KADEC: O gomeomorfismach nekotorych prostranstv Banacha.Dokl. Ak. Nauk SSSR, T XCII (1953), p. 465-468. MR 0059469 |
Reference:
|
[47] M. I. KADEC: O slaboj i silnoj schodimosti.Dokl. Ak. Nauk SSSR 122 (1958), No 1, p. 13. MR 0098977 |
Reference:
|
[48] M. I. KADEC: Topologičeskaja ekvivalentnosť vsech separabelnych prostranstv Banacha.Dokl. Ak. Nauk SSSR 167 (1966), N. 1, 23-25. MR 0201951 |
Reference:
|
[49] M. I. KADEC: O topologičeskoj ekvivalentnosti ravnomerno vypuklych prostranstv.Uspechi mat. nauk SSSR 10, 4 (1955), 137-142. MR 0073939 |
Reference:
|
[50] 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. |
Reference:
|
[51] M. I. KADEC: Uslovija differencirujemosti normy Banachova prostranstva.Uspechi mat. nauk SSSR T XX, 3 (123), 183-187. MR 0185416 |
Reference:
|
[52] S. KAKUTANI: Weak convergence in uniformly convex spaces.Tohoku Math. Journ. 45 (1939), 188-193. |
Reference:
|
[52a] T. KATO: Nonlinear semigroups and evolution equations.J. Math. Soc. Japan, Vol. 19 (1967), 508-520. Zbl 0163.38303, MR 0226230 |
Reference:
|
[53] W. A. KIRK: A fixed point theorem for mappings which do not increase distance.Amer. Math. Monthly 72 (1965), 1004-1006. MR 0189009 |
Reference:
|
[54] V. L. KLEE: Some characterizations of reflexivity.Revista Ci. Lima, 12 (1950), 15-23. Zbl 0040.35403, MR 0043364 |
Reference:
|
[55] V. L. KLEE: Convex bodies and periodic homeomorphisms in Hilbert spaces.Trans. of the Amer. Math. Soc. 74 (1953), 10-43. MR 0054850 |
Reference:
|
[56] V. L. KLEE: Extremal structure of convex sets II.Math. Zeit. 69 (1958), 90-104. Zbl 0079.12502, MR 0092113 |
Reference:
|
[57] V. L. KLEE: Mappings into normed linear spaces.Fundamenta Math. 49 (1960-61), 25-34. Zbl 0117.08303, MR 0126690 |
Reference:
|
[58] V. L. KLEE: Some new results on smoothness and rotundity in normed linear spaces.Math. Ann. 139, 51-63. Zbl 0092.11602, MR 0115076 |
Reference:
|
[59] V. L. KLEE: Convexity of Chebyshev sets.Math. Ann. 142, 292-304. Zbl 0091.27701 |
Reference:
|
[60] J. KOLOMÝ: On the differentiability of mappings in functional spaces.Comment. Math. Univ. Carol. 8, 2 (1967), 315-331. MR 0212569 |
Reference:
|
[61] J. KOLOMÝ: On the differentiability of mappings and convex functional.Comment. Math. Univ. Carol. 8, 4 (1967), 735-753. MR 0243348 |
Reference:
|
[62] 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). MR 0243348 |
Reference:
|
[63] J. DANEŠ J. KOLOMÝ: On the continuity and differentiability of convex functionals.Comment. Math. Univ. Carol. 9, 2 (1968), 329-350. MR 0239415 |
Reference:
|
[64] J. KOLOMÝ V. ZIZLER: Remarks on the differentiability of mappings in linear normed spaces.Comment. Math. Univ. Carol. 8, 4 (1967), 691-705. MR 0234279 |
Reference:
|
[65] G. KÖTHE: Topologische lineare Räume.Berlin 1960. |
Reference:
|
[66] J. KURZWEIL: On approximation in real Banach spaces.Studia Math. 14, 214-231. Zbl 0080.32602, MR 0068732 |
Reference:
|
[67] J. KURZWEIL: A characterization of analytic operations in real Banach spaces.Studia Math. 14 (1953), 82-83. Zbl 0052.34602, MR 0062948 |
Reference:
|
[68] S. LANG: Introduction to differentiable manifolds.New York 1962 (russian translation). Zbl 0103.15101, MR 0155257 |
Reference:
|
[69] J. LINDENSTRAUSS: On the modulus of smoothness and divergent series in Banach spaces.Michigan Math. J. 10 (1963), 241-252. Zbl 0115.10001, MR 0169061 |
Reference:
|
[70] J. LINDENSTRAUSS: On operators which attain their norm.Israel Journal of Mathem. 1 (1963), 139-148. Zbl 0127.06704, MR 0160094 |
Reference:
|
[71] J. LINDENSTRAUSS: On reflexive spaces having the metric approximation property.Israel Journal of Mathem. 3 (1965), 199-204. Zbl 0148.11302, MR 0205039 |
Reference:
|
[72] J. LINDENSTRAUSS: On nonseparable reflexive Banach spaces.Bull. of the Amer. Math. Soc. 1966, 967-970. Zbl 0156.36403, MR 0205040 |
Reference:
|
[73] J. LINDENSTRAUSS: On complemented subspace of $m$.Israel Journal of Mathem. 5 (1967), 153-156. MR 0222616 |
Reference:
|
[74] J. LINDENSTRAUSS: On extrene points in $l_1$.Israel Journal of Mathem. 4 (1966), 59-61. MR 0200701 |
Reference:
|
[75] J. LINDENSTRAUSS R. R. PHELPS: Extreme point properties of convex bodies in reflexive Banach spaces.Israel Journal of Mathem. 6, 1 (1968), 39-48. MR 0234260 |
Reference:
|
[76] A. R. LOVAGLIA: Locally uniformly convex Banach spaces.Trans. of the Amer. Math. Soc. 78 (1958), 225-238. MR 0066558 |
Reference:
|
[77] 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. |
Reference:
|
[78] S. MAZUR: Über konvexe Mengen in linearen normierten Räumen.Studia Math. 4 (1933), 70-84. Zbl 0008.31603 |
Reference:
|
[79] S. MAZUR: Über schwache Konvergenz in den Räumen $L^p$.Studia Math. 4 (1933), 128-133. |
Reference:
|
[80] D. MILMAN: On some criteria for the regularity of spaces of the type (B).C. R. Acad. Sci. USSR 20 (1938), 243-246. Zbl 0019.41601 |
Reference:
|
[81] I. NAMIOKA: Neighbourhoods of extreme points.Israel Journal of Mathem. 1967, N. 3, 145-152. MR 0221271 |
Reference:
|
[82] J. RAINWATER: Weak convergence of bounded sequences.Proc. of the Amer. Math. Soc. 1963, p. 999. Zbl 0117.08302, MR 0155171 |
Reference:
|
[83] M. M. RAO: Characterizing Hilbert space by smoothness.Reprinted from Proceedings. Series A, Vol. LXX, No. 1 (1967), 132-135. Zbl 0145.16201, MR 0211249 |
Reference:
|
[84] G. RESTREPO: Differentiable norms in Banach spaces.Bull. of the Amer. Math. Soc. 70 (1964), 413-414. MR 0161129 |
Reference:
|
[85] 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. Zbl 0098.08001, MR 0117530 |
Reference:
|
[85a] G. A. SUCHOMLINOV: Analitičeskije funkcionaly.Bjull. Moskov. univ. sekcija A, T 1 (1937), 1-19. |
Reference:
|
[86] R. SUNDARESAN: Smooth Banach spaces.Math. Ann. 173 (1967), Heft 3, 191-199. Zbl 0158.13701, MR 0218876 |
Reference:
|
[87] V. L. ŠMULJAN: O nekotorych geometričeskich svojstvach sfery v prostranstvach tipa B.Dokl. Ak. Nauk SSSR 24 (1939), 647-651. |
Reference:
|
[88] V. L. ŠMULJAN: O principu vkladok v prostranstve tipa B.Matem. Sb. 5 (47) (1939), 317-328. |
Reference:
|
[89] V. L. ŠMULJAN: O nekotorych geometričeskich svojstvach jediničnoj sfery prostranstva tipa B.Matem. Sb. 6 (48) (1939), 77-94. |
Reference:
|
[90] V. L. ŠMULJAN: O differencirujemosti normy v prostranstve Banacha.Dokl. Ak. Nauk SSSR 27 (1940), 643-648. |
Reference:
|
[91] V. L. ŠMULJAN: Sur la structure de la sphere unitaire dans l'espace de Banach.Matem. Sbornik 9 (1941), 545-572. |
Reference:
|
[92] S. TROJANSKIJ: Topologičeskaja ekvivalentnosť prostranstv $C_0 (\lambda )$, $l_1 (\lambda )$.Bull. de L. Acad. Pol. XV, 6 (1967), 389-396. |
Reference:
|
[93] M. M. VAJNBERG: Variacionnyje metody issledovanija nelinejnych operatorov.Moskva 1956. |
Reference:
|
[94] L. P. VLASOV: O Čebyševskich množstvach.Dokl. Ak. Nauk SSSR 173 (1967), 491-494. MR 0215059 |
Reference:
|
[95] L. P. VLASOV: Approximativno vypuklyje množestva v Banachovych prostranstvach.Dokl. Ak. Nauk SSSR 163 (1965), 18-21. |
Reference:
|
[96] L. P. VLASOV: O Čebyševskich množestvach v Banachovych prostranstvach.Dokl. Ak. Nauk SSSR 141, 19-20. |
Reference:
|
[97] L. P. VLASOV: Approximativno vypuklyje množestva v ravnomerno gladkich prostranstvach.Matem. Zametki 1 (1967), 443-450. |
Reference:
|
[98] J. WADA: Strict convexity and smoothness of normed spaces.Osaka J. Math. 10 (1958), 221-230. Zbl 0084.09804, MR 0100775 |
Reference:
|
[99] K. YOSHIDA: Functional analysis.(russian translation Moscow 1967). |
Reference:
|
[100] V. ZIZLER: On tne differentiability of mappings in Banach spaces.Comment. Math. Univ. Carol. 8, 3 (1967), 415-430. MR 0227772 |
. |