Each weakly countably determined Asplund space admits a Fréchet differentiable norm

DOI10.1017/S000497270000366XzbMath0642.46017OpenAlexW2008784872MaRDI QIDQ3784626

Martin Fabian

Publication date: 1987

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s000497270000366x

zbMATH Keywords

Fréchet differentiable normdual normweakly compactly generatedlocally uniformly rotundprojectional resolution of identityequivalent Gâteaux differentiable normweakly countably determined Asplund space

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Duality and reflexivity in normed linear and Banach spaces (46B10)

Related Items (10)

Stability of subdifferentials of nonconvex functions in Banach spaces ⋮ On equivalent characterizations of weakly compactly generated Banach spaces ⋮ Yet on linear structures of norm-attaining functionals on Asplund spaces ⋮ Examples concerning heredity problems of WCG Banach spaces ⋮ Banach spaces of continuous functions without norming Markushevich bases ⋮ On a classical renorming construction of V. Klee ⋮ An Asplund space with norming Markuševič basis that is not weakly compactly generated ⋮ On properties of compacta that do not reflect in small continuous images ⋮ Weak\(^*\) locally uniformly rotund norms and descriptive compact spaces ⋮ Smooth bump functions and the geometry of Banach spaces. A brief survey

Cites Work

• Borel selectors for upper semi-continuous set-valued maps
• Renormages de quelques \({\mathcal C}(K)\). (Renormings of some \({\mathcal C}(K)\) spaces)
• Banach spaces which are Asplund spaces
• Smoothness and its equivalents in weakly compactly generated Banach spaces
• The structure of weakly compact sets in Banach spaces
• On Borel Mappings and Baire Functions

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