Strong subdifferentiability of norms and geometry of Banach spaces

Gilles Godefroy; Vicente Montesinos; Václav Zizler

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 3, page 493-502
  • ISSN: 0010-2628

Abstract

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The strong subdifferentiability of norms (i.eȯne-sided differentiability uniform in directions) is studied in connection with some structural properties of Banach spaces. It is shown that every separable Banach space with nonseparable dual admits a norm that is nowhere strongly subdifferentiable except at the origin. On the other hand, every Banach space with a strongly subdifferentiable norm is Asplund.

How to cite

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Godefroy, Gilles, Montesinos, Vicente, and Zizler, Václav. "Strong subdifferentiability of norms and geometry of Banach spaces." Commentationes Mathematicae Universitatis Carolinae 36.3 (1995): 493-502. <http://eudml.org/doc/247756>.

@article{Godefroy1995,
abstract = {The strong subdifferentiability of norms (i.eȯne-sided differentiability uniform in directions) is studied in connection with some structural properties of Banach spaces. It is shown that every separable Banach space with nonseparable dual admits a norm that is nowhere strongly subdifferentiable except at the origin. On the other hand, every Banach space with a strongly subdifferentiable norm is Asplund.},
author = {Godefroy, Gilles, Montesinos, Vicente, Zizler, Václav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {strong subdifferentiability of norms; Asplund spaces; renormings; weak compact generating; Asplund spaces; renormings; weak compact generating; strong subdifferentiability of norms; structural properties of Banach spaces; separable Banach space with nonseparable dual},
language = {eng},
number = {3},
pages = {493-502},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Strong subdifferentiability of norms and geometry of Banach spaces},
url = {http://eudml.org/doc/247756},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Godefroy, Gilles
AU - Montesinos, Vicente
AU - Zizler, Václav
TI - Strong subdifferentiability of norms and geometry of Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 3
SP - 493
EP - 502
AB - The strong subdifferentiability of norms (i.eȯne-sided differentiability uniform in directions) is studied in connection with some structural properties of Banach spaces. It is shown that every separable Banach space with nonseparable dual admits a norm that is nowhere strongly subdifferentiable except at the origin. On the other hand, every Banach space with a strongly subdifferentiable norm is Asplund.
LA - eng
KW - strong subdifferentiability of norms; Asplund spaces; renormings; weak compact generating; Asplund spaces; renormings; weak compact generating; strong subdifferentiability of norms; structural properties of Banach spaces; separable Banach space with nonseparable dual
UR - http://eudml.org/doc/247756
ER -

References

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