On extension of isometries and approximate isometries between unit spheres

DOI10.1016/j.jmaa.2008.11.034zbMath1160.46305OpenAlexW2116672067MaRDI QIDQ1018683

Rui Liu, Lun Zhang

Publication date: 20 May 2009

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2008.11.034

zbMATH Keywords

isometric extensionAM-space\(L^{1}\)-space

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20)

Related Items (14)

The isometric extension problem between unit spheres of two separable Banach spaces ⋮ Extension of quasi-Hölder embeddings between unit spheres of \(p\)-normed spaces ⋮ On the quasi-Figiel problem and extension of \(\varepsilon\)-isometry on unit sphere of \(\mathcal{L}_{\infty, 1^+}\) space ⋮ On the Figiel type problem and extension of \(\varepsilon\)-isometry between unit spheres ⋮ Unnamed Item ⋮ The slice approximating property and Figiel-type problem on unit spheres ⋮ On isometries and Tingley’s problem for the spaces $T[\theta , \mathcal{S}_{\alpha }$, $1 \leqslant\alpha \lt \omega _{1}$] ⋮ Some new properties and isometries on the unit spheres of generalized James spaces \(J_{p}\) ⋮ On extension of isometries on the unit spheres of \(L^p\)-spaces for \(0 < p \leq 1\) ⋮ Extension of isometries on the unit sphere of \(L^p\) spaces ⋮ Sharp corner points and isometric extension problem in Banach spaces ⋮ A note on the Mazur-Ulam property of almost-CL-spaces ⋮ Isometries between normed spaces which are surjective on a sphere ⋮ A note on extension of isometric embedding from a Banach space \(E\) into the universal space \(\ell _{\infty }(\Gamma )\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The isometric extension problem in the unit spheres of \(l^p(\Gamma)(p>1)\) type spaces
• Isometries on unit sphere of (\(\ell^{\beta_n}\))
• On extension of isometries between unit spheres of \(L_{p}(\mu )\) and \(L_{p}(\nu ,H)\) (\(1< p \neq 2\), \(H\) is a Hilbert space)
• Almost isometries on the unit ball of \(\ell _ 1\)
• Properties of isometric mappings
• On the extension of isometries between unit spheres of \(E\) and \(C(\Omega)\).
• Almost isometries of balls
• Isometries of the unit sphere
• On nonlinear perturbations of isometries
• 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
• The 1-Lipschitz mapping between the unit spheres of two Hilbert spaces can be extended to a real linear isometry of the whole space
• Approximate Isometries on Finite-Dimensional Normed Spaces
• A remark on quasi-isometries
• On extension of isometries between unit spheres of 𝐴𝐿_{𝑝}-spaces (0<𝑝<∞)
• On approximate isometries
• On perturbations and extensions of isometric operators

This page was built for publication: On extension of isometries and approximate isometries between unit spheres