Algebraic properties of isometries between groups of invertible elements in Banach algebras

DOI10.1016/J.JMAA.2010.11.027zbMath1216.46007arXiv0905.1047OpenAlexW1984335530MaRDI QIDQ624557

Osamu Hatori

Publication date: 9 February 2011

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

Full work available at URL: https://arxiv.org/abs/0905.1047

zbMATH Keywords

Banach algebrasMazur-Ulam theoremisometriesgroups of invertible elements

Mathematics Subject Classification ID

Linear operators on Banach algebras (47B48) Isometric theory of Banach spaces (46B04)

Related Items (7)

Isometries of the unitary group ⋮ Isometries and maps compatible with inverted Jordan triple products on groups ⋮ Stability of isometries between groups of invertible elements in Banach algebras ⋮ Tingley's problem on finite von Neumann algebras ⋮ Isometries of the unitary groups and Thompson isometries of the spaces of invertible positive elements in \(C^\ast\)-algebras ⋮ Surjective isometries between sets of invertible elements in unital Jordan-Banach algebras ⋮ The solution of Tingley's problem for the operator norm unit sphere of complex \(n\times n\) matrices

Cites Work

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• Reflections and a generalization of the Mazur-Ulam theorem
• Additive maps on standard operator algebras preserving invertibilities or zero divisors.
• Isometries between groups of invertible elements in Banach algebras
• The Uniqueness of Multiplication in Function Algebras
• Thompson isometries of the space of invertible positive operators
• A Proof of the Mazur-Ulam Theorem
• From geometry to invertibility preservers

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