A Bound-Two Isomorphism Between C(X) Banach Spaces

DOI10.2307/2040542zbMath0317.46025OpenAlexW4236475227MaRDI QIDQ4078575

Henry B. Cohen

Publication date: 1975

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2040542

Mathematics Subject Classification ID

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

Related Items (26)

Isomorphisms of AC(σ) spaces ⋮ An optimal nonlinear extension of Banach-Stone theorem ⋮ An optimal linear approximation for a class of nonlinear operators between uniform algebras ⋮ A vector-valued Banach-Stone theorem with distortion \(\sqrt{2}\) ⋮ Automatic continuity of linear maps on spaces of continuous functions ⋮ 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 ⋮ A solution to the Cambern problem for finite-dimensional Hilbert spaces ⋮ Weak forms of Banach-Stone theorem for \(C_{0}(K,X)\) spaces via the \(\alpha\)th derivatives of \(K\) ⋮ A stronger form of Banach-Stone theorem to 𝐶₀(𝐾,𝑋) spaces including the cases 𝑋=𝑙_{𝑝}², 1<𝑝<∞ ⋮ Linear isometries between subspaces of continuous functions ⋮ On non-linear \(\varepsilon\)-isometries between the positive cones of certain continuous function spaces ⋮ A generalized Banach-Stone theorem for \(C_{0}(K,X)\) spaces via the modulus of convexity of \(X^\ast\) ⋮ Continuous maps induced by embeddings of \(C_{0}(K)\) spaces into \(C_{0}(S, X)\) spaces ⋮ SMALL-BOUND ISOMORPHISMS OF FUNCTION SPACES ⋮ A second-dual method for C(X) isomorphisms ⋮ The minimum principle for affine functions and isomorphisms of continuous affine function spaces ⋮ An Amir-Cambern theorem for quasi-isometries of \(C_0(K,X)\) spaces ⋮ Isomorphisms from extremely regular subspaces of \(C_0(K)\) into \(C_0(S,X)\) spaces ⋮ Isomorphisms of subspaces of vector-valued 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) ⋮ Isomorphisms of spaces of affine continuous complex functions ⋮ Non-surjective coarse version of the Banach-Stone theorem ⋮ A weak vector-valued Banach-Stone theorem ⋮ Optimal extensions of the Banach-Stone theorem

This page was built for publication: A Bound-Two Isomorphism Between C(X) Banach Spaces