Tingley's problem for \(p\)-Schatten von Neumann classes

DOI10.4171/JST/313zbMath1472.46006arXiv1803.00763OpenAlexW3033474240MaRDI QIDQ2662226

Francisco J. Fernández-Polo, Enrique Jordá, Antonio M. Peralta

Publication date: 9 April 2021

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.00763

zbMATH Keywords

Tingley's problemextension of isometries\(p\)-Schatten-von Neumann operators

Mathematics Subject Classification ID

Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Isometric theory of Banach spaces (46B04) Operator ideals (47L20) Transformers, preservers (linear operators on spaces of linear operators) (47B49)

Related Items (10)

Can one identify two unital JB*-algebras by the metric spaces determined by their sets of unitaries? ⋮ Tingley's problem for complex Banach spaces which do not satisfy the Hausdorff distance condition ⋮ Unnamed Item ⋮ Exploring new solutions to Tingley’s problem for function algebras ⋮ Extension of isometries from the unit sphere of a rank-2 Cartan factor ⋮ A Tingley's type problem in \(n\)-normed spaces ⋮ Tingley's problems on uniform algebras ⋮ The Mazur–Ulam property for commutative von Neumann algebras ⋮ On the Mazur-Ulam property for the space of Hilbert-space-valued continuous functions ⋮ A note on Tingley’s problem and Wigner’s theorem in the unit sphere of ^∞(Γ)-type spaces

Cites Work

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• The solution of Tingley's problem for the operator norm unit sphere of complex \(n\times n\) matrices
• Spherical isometries of finite dimensional \(C^{\ast}\)-algebras
• Tingley's problem on finite von Neumann algebras
• The isometric extension problem in the unit spheres of \(l^p(\Gamma)(p>1)\) type spaces
• On extension of isometries on the unit spheres of \(L^p\)-spaces for \(0 < p \leq 1\)
• Extending surjective isometries defined on the unit sphere of \(\ell_\infty(\Gamma)\)
• Extension of isometries on unit sphere of \(L^\infty\)
• Tingley's problem through the facial structure of operator algebras
• Extension of isometries between the unit spheres of normed space \(E\) and \(C(\Omega)\)
• On isometric extension problem between two unit spheres
• On certain automorphisms of sets of partial isometries.
• On the extension of isometries between the unit spheres of von Neumann algebras
• A solution to Tingley's problem for isometries between the unit spheres of compact \(\mathrm C^*\)-algebras and \(\mathrm {JB}^*\)-triples
• Extension of isometries on the unit sphere of \(L^p\) spaces
• Low rank compact operators and Tingley's problem
• Isometries of the unit sphere
• Generalization of Wigner's unitary-antiunitary theorem for indefinite inner product spaces
• Tingley's problem through the facial structure of an atomic \(JBW^*\)-triple
• Tingley's problem for spaces of trace class operators
• 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
• \(c_ p\)
• 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
• A survey on Tingley’s problem for operator algebras
• Perturbation Bounds for Matrix Eigenvalues
• Symmetry Groups in Quantum Mechanics and the Theorem of Wigner on the Symmetry Transformations
• A generalization of Wigner’s unitary–antiunitary theorem to Hilbert modules
• On the extension of isometries between the unit spheres of a C*-algebra and 𝐵(𝐻)
• The Mazur–Ulam property for the space of complex null sequences
• Distance between Hermitian operators in Schatten classes
• Isometries on positive operators of unit norm

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