Smoothness in weakly compactly generated Banach spaces

DOI10.1016/0022-1236(83)90073-3zbMath0517.46010OpenAlexW1996198979MaRDI QIDQ1053225

J. H. M. Whitfield, Stanimir Troyanski, Václav Zizler, Gilles Godefroy

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1016/0022-1236(83)90073-3

zbMATH Keywords

Radon-Nikodym propertyweakly compactly generated Banach spaceCk-smooth partition of unityconstruction of Frechet smooth normsFrechet-smooth normlocally uniformly rotund dual norms

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Isomorphic theory (including renorming) of Banach spaces (46B03) Radon-Nikodým, Kre?n-Milman and related properties (46B22) Duality and reflexivity in normed linear and Banach spaces (46B10)

Related Items (19)

Super WCG Banach spaces ⋮ Problèmes de renormages. (Renorming problems) ⋮ Smooth partitions of unity and approximating norms in Banach spaces ⋮ Smooth partitions of unity in Banach spaces ⋮ Strong solutions and mild solutions for Sturm-Liouville differential inclusions ⋮ Approximation by Lipschitz, \(C^p\) smooth functions on weakly compactly generated Banach spaces ⋮ Extensions of vector-valued functions with preservation of derivatives ⋮ Renorming in the space of Bochner integrable functions \(L_ 1(\mu{},X)\) ⋮ Smoothing of bump functions ⋮ Smooth partitions of unity in preduals of WCG spaces ⋮ Smooth partitions of unity on Banach spaces ⋮ Smooth Approximations in Banach Spaces ⋮ Polyhedrality in Orlicz spaces ⋮ Locally flat Banach spaces ⋮ A Banach space admits a locally uniformly rotund norm if its dual is a Vašák space ⋮ Approximation by functions with bounded derivative on Banach spaces ⋮ On dual locally uniformly rotund norms ⋮ On weakly Lindelöf Banach spaces ⋮ Smooth bump functions and the geometry of Banach spaces. A brief survey

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Norms with locally Lipschitzian derivatives
• Some remarks on weakly compactly generated Banach spaces
• Geometry of Banach spaces. Selected topics
• On the heredity of weak compact generating
• Espaces de Banachs faiblement K-analytiques
• Smoothness and its equivalents in weakly compactly generated Banach spaces
• The structure of weakly compact sets in Banach spaces
• On one generalization of weakly compactly generated Banach spaces
• On locally uniformly convex and differentiable norms in certain non-separable Banach spaces
• Smooth partitions of unity on some non-separable Banach spaces

This page was built for publication: Smoothness in weakly compactly generated Banach spaces