# Uniform Eberlein Compacta and Uniformly Gâteaux Smooth Norms

Fabian, Marián; Hájek, Petr; Zizler, Václav

Serdica Mathematical Journal (1997)

- Volume: 23, Issue: 3-4, page 351-362
- ISSN: 1310-6600

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topFabian, 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 -

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