An optimal nonlinear extension of Banach-Stone theorem

DOI10.1016/J.JFA.2016.07.008zbMath1353.46007OpenAlexW2501718230MaRDI QIDQ306558

Elói Medina Galego, André Luis Porto da Silva

Publication date: 31 August 2016

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

Full work available at URL: https://doi.org/10.1016/j.jfa.2016.07.008

zbMATH Keywords

spaces of continuous functionsnonlinear Banach-Stone theorem

Mathematics Subject Classification ID

Isomorphic theory (including renorming) of Banach spaces (46B03) Banach spaces of continuous, differentiable or analytic functions (46E15)

Related Items (15)

Complexity of distances: reductions of distances between metric and Banach spaces ⋮ An optimal linear approximation for a class of nonlinear operators between uniform algebras ⋮ A vector-valued Banach-Stone theorem with distortion \(\sqrt{2}\) ⋮ A wider nonlinear extension of Banach-Stone theorem to 𝐶₀(𝐾,𝑋) spaces which is optimal for 𝑋=ℓ_{𝑝}, 2≤𝑝<∞ ⋮ A stronger form of Banach-Stone theorem to 𝐶₀(𝐾,𝑋) spaces including the cases 𝑋=𝑙_{𝑝}², 1<𝑝<∞ ⋮ On perturbed isometries between the positive cones of certain continuous function spaces ⋮ On non-linear \(\varepsilon\)-isometries between the positive cones of certain continuous function spaces ⋮ SMALL-BOUND ISOMORPHISMS OF FUNCTION SPACES ⋮ Unnamed Item ⋮ An Amir-Cambern theorem for quasi-isometries of \(C_0(K,X)\) spaces ⋮ Isomorphisms of subspaces of vector-valued continuous functions ⋮ 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) ⋮ Non-surjective coarse version of the Banach-Stone theorem

Cites Work

• Coarse version of the Banach-Stone theorem
• Affine properties and injectivity of quasi-isometries
• On isomorphisms of continuous function spaces
• Perturbations of isometries between Banach spaces
• Nonlinear generalizations of the Banach-Stone theorem
• A Bound-Two Isomorphism Between C(X) Banach Spaces
• Perturbations of isometries between C(K)-spaces
• On Isomorphisms with Small Bound

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