Can one identify two unital JB*-algebras by the metric spaces determined by their sets of unitaries?

DOI10.1080/03081087.2021.2003745zbMath1526.46004arXiv2005.04794OpenAlexW3217766560MaRDI QIDQ6039173

María Cueto-Avellaneda, Antonio M. Peralta

Publication date: 3 May 2023

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.04794

zbMATH Keywords

isometryJordan \(*\)-isomorphismextension of isometries\(\mathrm{JB}^*\)-algebra\(\mathrm{JBW}^*\)-algebraunitary set

Mathematics Subject Classification ID

Isometric theory of Banach spaces (46B04) Jordan structures on Banach spaces and algebras (17C65) Nonassociative selfadjoint operator algebras (46L70)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On a generalized Mazur-Ulam question: Extension of isometries between unit spheres of Banach spaces
• Extending surjective isometries defined on the unit sphere of \(\ell_\infty(\Gamma)\)
• Tingley's problem through the facial structure of operator algebras
• On the groups isomorphism of unitary groups in \(AW^*\)-algebras
• A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces
• The Gelfand-Naimark theorem for \(JB^ *\)-triples
• Jordan \(C^*\)-algebras
• A holomorphic characterization of Jordan \(C^*\)-algebras
• The Mazur-Ulam property for two-dimensional somewhere-flat spaces
• 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
• Low rank compact operators and Tingley's problem
• Isometries of the unit sphere
• Isometries of JB-algebras
• Isometries and maps compatible with inverted Jordan triple products on groups
• Metric characterisation of unitaries in JB\(^*\)-algebras
• Tingley's problem through the facial structure of an atomic \(JBW^*\)-triple
• One-parameter semigroups of orthogonality preservers of JB*-algebras
• One-parameter groups of orthogonality preservers on \(C^*\)-algebras
• Extension of isometries from the unit sphere of a rank-2 Cartan factor
• Isometries of the unitary groups and Thompson isometries of the spaces of invertible positive elements in \(C^\ast\)-algebras
• On the Mazur-Ulam property for the space of Hilbert-space-valued continuous functions
• Tingley's problem for spaces of trace class operators
• A note on unitary operators in \(C^ *\)-algebras
• A reflection on Tingley's problem and some applications
• On the geometry of projections in certain operator algebras
• Tingley's problem for \(p\)-Schatten von Neumann classes
• Isometries of the unitary group
• DERIVATIONS ON REAL AND COMPLEX JB*-TRIPLES
• Surjective isometries between real JB*-triples
• A survey on Tingley’s problem for operator algebras
• Structure of the predual of a JBW*-triple.
• BOUNDED DERIVATIONS OF JB^* - TRIPLES
• Real Isometries between J B ∗ -Triples
• On Isometries of Jordan Algebras
• A Vidav theorem for Banach Jordan algebras
• Non-Associative Normed Algebras
• The Mazur–Ulam property for the space of complex null sequences
• ON THE EXTENSION OF ISOMETRIES BETWEEN THE UNIT SPHERES OF A -TRIPLE AND A BANACH SPACE
• Mankiewicz’s theorem and the Mazur–Ulam property for $\mathbf {C}^*$-algebras
• The Mazur–Ulam property for commutative von Neumann algebras
• On the Extension Problems of Isometric and Nonexpansive Mappings
• Non-Associative Normed Algebras