Second-Order Gâteaux Differentiable Bump Functions and Approximations in Banach Spaces

DOI10.4153/CJM-1993-032-9zbMath0796.46005MaRDI QIDQ4290170

David P. McLaughlin, R. A. Poliquin, Jon Vanderwerff, Václav Zizler

Publication date: 4 October 1994

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

locally uniformly rotund normsapproximations of convex functions by twice Gâteaux differentiable convex functionsBanach spaces which have the Radon-Nikodym property and admit twice Gâteaux differentiable bump functionslimits of \(C^ k\)-smooth norms

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) 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) Derivatives of functions in infinite-dimensional spaces (46G05)

Related Items (10)

Uniformly differentiable bump functions ⋮ Higher order Gateaux smooth bump functions on Banach spaces ⋮ Sets of differentials and smoothness of convex functions ⋮ Approximation by Lipschitz, \(C^p\) smooth functions on weakly compactly generated Banach spaces ⋮ 𝐶^{𝑘}-smooth approximations of LUR norms ⋮ On regularization in Banach spaces ⋮ Approximation by functions with bounded derivative on Banach spaces ⋮ Structural implications of norms with Hölder right-hand derivatives. ⋮ Extensions of uniformly smooth norms on Banach spaces ⋮ Smooth bump functions and the geometry of Banach spaces. A brief survey

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