Extension of isometries on the unit sphere of \(l ^{p }(\Gamma )\) space

DOI10.1007/S11425-010-0028-4zbMath1200.46016OpenAlexW2165498677MaRDI QIDQ977272

Xi Nian Fang, Jian-Hua Wang

Publication date: 21 June 2010

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-010-0028-4

zbMATH Keywords

isometryisometric extension1-Lipschitz mapping\(l ^{p }(\Gamma )\) space

Mathematics Subject Classification ID

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

Related Items (10)

The isometric extension problem between unit spheres of two separable Banach spaces ⋮ The Mazur-Ulam property for two-dimensional somewhere-flat spaces ⋮ Surjective isometries on Banach sequence spaces: a survey ⋮ Isometries and additive mapping on the unit spheres of normed spaces ⋮ Unnamed Item ⋮ Order type Tingley's problem for type \(I\) finite von Neumann algebras ⋮ On a variant of Tingley's problem for some function spaces ⋮ Extension of isometries on the unit sphere of \(L^p\) spaces ⋮ Sharp corner points and isometric extension problem in Banach spaces ⋮ Some remarks on generalised lush spaces

Cites Work

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• On the extension of isometries between unit spheres of \(E\) and \(C(\Omega)\).
• Isometries of the unit sphere
• On extension of isometries between unit spheres of \(\mathcal L^{\infty}(\Gamma)\)-type space and a Banach space \(E\)
• The isometric extension of the into mapping from a \(\mathcal{L}^{\infty}(\Gamma)\)-type space to some Banach space
• The representation theorem of onto isometric mappings between two unit spheres of \(l^\infty\)-type spaces and the application on isometric extension problem
• A geometric characterization of the nonlinear Schrödinger equation
• The representation theorem of onto isometric mappings between two unit spheres of \(l^1(\Gamma)\) type spaces and the application to the isometric extension problem
• On extension of isometries between unit spheres of 𝐴𝐿_{𝑝}-spaces (0<𝑝<∞)
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