A note on the stability of nonsurjective 𝜖-isometries of Banach spaces

DOI10.1090/proc/15110zbMath1472.46004OpenAlexW3014385065MaRDI QIDQ5119236

Yun Bai Dong, Li Xing Cheng

Publication date: 3 September 2020

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

Full work available at URL: https://doi.org/10.1090/proc/15110

zbMATH Keywords

isometryweak stability

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Isometric theory of Banach spaces (46B04)

Related Items (15)

On non-surjective \(\varepsilon\)-isometric embeddings between Hausdorff metric spaces of compact convex subsets ⋮ On the quasi-Figiel problem and extension of \(\varepsilon\)-isometry on unit sphere of \(\mathcal{L}_{\infty, 1^+}\) space ⋮ A universal inequality for stability of coarse Lipschitz embeddings ⋮ Hyers–Ulam stability of non-surjective isometries between subspaces of continuous functions ⋮ On the Figiel type problem and extension of \(\varepsilon\)-isometry between unit spheres ⋮ The slice approximating property and Figiel-type problem on unit spheres ⋮ On a universal inequality for approximate phase isometries ⋮ Stability of \(\varepsilon \)-isometries and their symmetrizations on the positive cones of \(c_0\) ⋮ Hyers-Ulam stability of isometries on bounded domains. II. ⋮ On perturbations of two general equations in several variables ⋮ A convex set-valued version of the Mazur-Ulam theorem on Asplund spaces ⋮ On the generalized Hyers-Ulam stability of a functional equation and its consequences ⋮ On stability and weak-star stability of \(\varepsilon\)-isometries ⋮ Ulam stability of functional equations in 2-Banach spaces via the fixed point method ⋮ On \(\mathcal{U}\)-weak stability of coarse isometries between \(L^p\) spaces

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