Coarse version of the Banach-Stone theorem

DOI10.1016/J.JMAA.2010.11.012zbMath1214.46012arXiv1005.0937OpenAlexW2091865429MaRDI QIDQ626189

Rafał Górak

Publication date: 22 February 2011

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

Full work available at URL: https://arxiv.org/abs/1005.0937

zbMATH Keywords

coarse mapsnon-linear Banach-Stone type theorems

Mathematics Subject Classification ID

Banach spaces of continuous, differentiable or analytic functions (46E15) Continuous and differentiable maps in nonlinear functional analysis (46T20) Nonlinear classification of Banach spaces; nonlinear quotients (46B80)

Related Items (8)

An optimal nonlinear extension of Banach-Stone theorem ⋮ An optimal linear approximation for a class of nonlinear operators between uniform algebras ⋮ A wider nonlinear extension of Banach-Stone theorem to 𝐶₀(𝐾,𝑋) spaces which is optimal for 𝑋=ℓ_{𝑝}, 2≤𝑝<∞ ⋮ Low distortion embeddings of some metric graphs into Banach spaces ⋮ An Amir-Cambern theorem for quasi-isometries of \(C_0(K,X)\) spaces ⋮ Nonlinear embeddings of spaces of continuous functions ⋮ Quasi-isometries on subsets of 𝐶₀(𝐾) and 𝐶₀⁽¹⁾(𝐾) spaces which determine 𝐾 ⋮ Best constants of Banach-Stone type theorems in subgroups of 𝐶(𝐾)

Cites Work

• Affine properties and injectivity of quasi-isometries
• On nonlinear perturbations of isometries
• Nonlinear generalizations of the Banach-Stone theorem
• Perturbations of isometries between C(K)-spaces
• Stability of Isometries on Banach Spaces
• On Isomorphisms with Small Bound
• Isometries and approximate isometries

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