On weakly locally uniformly rotund Banach spaces

DOI10.1006/jfan.1998.3376zbMath0927.46010OpenAlexW2077650977MaRDI QIDQ1288248

Manuel Valdivia, José Orihuela, Stanimir Troyanski, Aníbal Moltó

Publication date: 11 May 1999

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1998.3376

zbMATH Keywords

LURweakly locally uniformly rotundlocally uniformly rotundWLUR

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Isomorphic theory (including renorming) of Banach spaces (46B03)

Related Items (17)

Metrization theory and the Kadec property ⋮ Network characterization of Gul'ko compact spaces and their relatives ⋮ Locally uniformly convex norms in Banach spaces and their duals ⋮ Borel measurability of separately continuous functions. II. ⋮ On \(\mathcal T_p\)-locally uniformly rotund norms ⋮ DUAL DIFFERENTIATION SPACES ⋮ On Gruenhage spaces, separating \(\sigma\)-isolated families, and their relatives ⋮ Absolute Souslin-\({\mathcal F}\) spaces and other weak-invariants of the norm topology ⋮ A dual differentiation space without an equivalent locally uniformly rotund norm ⋮ Renormings of \(C(K)\) spaces ⋮ Compact convex sets that admit a lower semicontinuous strictly convex function ⋮ A stability property for locally uniformly rotund renorming ⋮ Some generalizations of locally uniform rotundity ⋮ On dual locally uniformly rotund norms ⋮ Borel measurability of separately continuous functions ⋮ Weak\(^*\) locally uniformly rotund norms and descriptive compact spaces ⋮ Smooth bump functions and the geometry of Banach spaces. A brief survey

Cites Work

• On a property of the norm which is close to locally uniform rotundity
• \(\sigma\)-fragmentability of multivalued maps and selection theorems
• A Banach space admits a locally uniformly rotund norm if its dual is a Vašák space
• Generic differentiability of convex functions on the dual of a Banach space
• The dual of every Asplund space admits a projectional resolution of the identity
• Locally Uniformly Rotund Renorming and Injections Into c₀(Γ)
• Internal characterization of fragmentable spaces
• σ‐fragmentable Banach spaces
• Baire Class 1 Selectors for Upper Semicontinuous Set-Valued Maps
• Smooth bump functions and geomentry of Banach spaces
• Čech analytic and almost $K$-descriptive spaces
• Weak Covering Properties of Weak Topologies
• Locally uniformly rotund renorming and fragmentability
• Fragmentability and Sigma-Fragmentability of Banach Spaces
• Trees in Renorming Theory
• Kadec norms and Borel sets in a Banach space
• Locally uniformly rotund norms
• Topological Properties of the Set of Norm-Attaining Linear Functionals
• σ‐fragmentability and analyticity
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