Uniformly Gâteaux smooth approximations on \(c_0(\varGamma)\)

DOI10.1016/j.jmaa.2008.05.008zbMath1170.46068OpenAlexW2024012950MaRDI QIDQ2518756

Michal Johanis, Petr Hájek

Publication date: 16 January 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2008.05.008

zbMATH Keywords

approximation\(C^{\infty }\)-Fréchet smoothnessuniform Gâteaux smoothness

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Continuous and differentiable maps in nonlinear functional analysis (46T20) Derivatives of functions in infinite-dimensional spaces (46G05)

Related Items (8)

On smooth extensions of vector-valued functions defined on closed subsets of Banach spaces ⋮ Invariance of closed convex cones for stochastic partial differential equations ⋮ Renormings preserving local geometry at countably many points in spheres of Banach spaces and applications ⋮ Smooth extension of functions on a certain class of non-separable Banach spaces ⋮ On some problems on smooth approximation and smooth extension of Lipschitz functions on Banach-Finsler manifolds ⋮ Smooth approximations ⋮ Density and extension of differentiable functions on metric measure spaces ⋮ Approximation of Lipschitz functions preserving boundary values

Cites Work

• Smooth Banach spaces, weak Asplund spaces and monotone or usco mappings
• Uniformly differentiable bump functions
• Uniformly smooth partitions of unity on superreflexive Banach spaces
• Trees in Renorming Theory
• On uniformly Gâteaux smooth C (n)-smooth norms on separable Banach spaces
• Higher order Gateaux smooth bump functions on Banach spaces
• Functional analysis and infinite-dimensional geometry
• The structure of uniformly Gâteaux smooth Banach spaces
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