Uniform Eberlein Compacta and Uniformly Gâteaux Smooth Norms

Fabian, Marián, Hájek, Petr, and Zizler, Václav. "Uniform Eberlein Compacta and Uniformly Gâteaux Smooth Norms." Serdica Mathematical Journal 23.3-4 (1997): 351-362. <http://eudml.org/doc/11622>.

@article{Fabian1997,
abstract = {* Supported by grants: AV ĈR 101-95-02, GAĈR 201-94-0069 (Czech Republic) and NSERC 7926 (Canada).It is shown that the dual unit ball BX∗ of a Banach space X∗ in its weak star topology is a uniform Eberlein compact if and only if X admits a uniformly Gâteaux smooth norm and X is a subspace of a weakly compactly generated space. The bidual unit ball BX∗∗ of a Banach space X∗∗ in its weak star topology is a uniform Eberlein compact if and only if X admits a weakly uniformly rotund norm. In this case X admits a locally uniformly rotund and Fréchet differentiable norm. An Eberlein compact K is a uniform Eberlein compact if and only if C(K) admits a uniformly Gˆateaux differentiable norm.},
author = {Fabian, Marián, Hájek, Petr, Zizler, Václav},
journal = {Serdica Mathematical Journal},
keywords = {Uniform Eberlein Compacta; Uniform Gâteaux Smooth Norms; Weak Compact Generating; uniform Eberlein compact; Gâteaux smooth norm; weakly compactly generated space; locally uniformly rotund and Fréchet differentiable norm},
language = {eng},
number = {3-4},
pages = {351-362},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Uniform Eberlein Compacta and Uniformly Gâteaux Smooth Norms},
url = {http://eudml.org/doc/11622},
volume = {23},
year = {1997},
}

TY - JOUR
AU - Fabian, Marián
AU - Hájek, Petr
AU - Zizler, Václav
TI - Uniform Eberlein Compacta and Uniformly Gâteaux Smooth Norms
JO - Serdica Mathematical Journal
PY - 1997
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 23
IS - 3-4
SP - 351
EP - 362
AB - * Supported by grants: AV ĈR 101-95-02, GAĈR 201-94-0069 (Czech Republic) and NSERC 7926 (Canada).It is shown that the dual unit ball BX∗ of a Banach space X∗ in its weak star topology is a uniform Eberlein compact if and only if X admits a uniformly Gâteaux smooth norm and X is a subspace of a weakly compactly generated space. The bidual unit ball BX∗∗ of a Banach space X∗∗ in its weak star topology is a uniform Eberlein compact if and only if X admits a weakly uniformly rotund norm. In this case X admits a locally uniformly rotund and Fréchet differentiable norm. An Eberlein compact K is a uniform Eberlein compact if and only if C(K) admits a uniformly Gˆateaux differentiable norm.
LA - eng
KW - Uniform Eberlein Compacta; Uniform Gâteaux Smooth Norms; Weak Compact Generating; uniform Eberlein compact; Gâteaux smooth norm; weakly compactly generated space; locally uniformly rotund and Fréchet differentiable norm
UR - http://eudml.org/doc/11622
ER -