Smooth Approximations in Banach Spaces

DOI10.2307/2159572zbMath0812.46005OpenAlexW4239644472MaRDI QIDQ4005735

Jon Vanderwerff

Publication date: 27 September 1992

Full work available at URL: https://doi.org/10.2307/2159572

zbMATH Keywords

Lipschitz derivativelocally uniformly convex normLUC\(C^ 1\)-smooth partitions of unity

Mathematics Subject Classification ID

Function spaces in general topology (54C35) Geometry and structure of normed linear spaces (46B20) Isomorphic theory (including renorming) of Banach spaces (46B03) Counterexamples in general topology (54G20) Isometric theory of Banach spaces (46B04)

Related Items (10)

Approximation by smooth functions with no critical points on separable Banach spaces ⋮ Smooth partitions of unity and approximating norms in Banach spaces ⋮ Smooth partitions of unity in Banach spaces ⋮ Almost Lie structures on an anchored Banach bundle ⋮ Smooth partitions of unity in preduals of WCG spaces ⋮ Second Order Differentiability of Convex Functions in Banach Spaces ⋮ On regularization in Banach spaces ⋮ Approximation by functions with bounded derivative on Banach spaces ⋮ Smooth approximations without critical points of continuous mappings between Banach spaces, and diffeomorphic extractions of sets ⋮ Smooth bump functions and the geometry of Banach spaces. A brief survey

Cites Work

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• The three space problem for smooth partitions of unity and \(C(K)\) spaces
• Smoothness in weakly compactly generated Banach spaces
• Problèmes de renormages. (Renorming problems)
• Renormages de quelques \({\mathcal C}(K)\). (Renormings of some \({\mathcal C}(K)\) spaces)
• Smooth partitions of unity in preduals of WCG spaces
• Geometry of Banach spaces. Selected topics
• A Banach space admits a locally uniformly rotund norm if its dual is a Vašák space
• Locally Uniformly Rotund Renorming and Injections Into c₀(Γ)
• On a dual locally uniformly rotund norm on a dual Vašák space
• Trees in Renorming Theory
• A Counterexample to Several Questions about Scattered Compact Spaces
• A locally uniformly convex renorming for certain ℒ(K)
• Smooth partitions of unity on some non-separable Banach spaces
• Geometry and nonlinear analysis in Banach spaces

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