A Mazur-Ulam theorem for normed gyrolinear spaces

DOI10.1090/conm/687/13733zbMath1385.46015OpenAlexW4248595946MaRDI QIDQ5351752

Toshikazu Abe

Publication date: 30 August 2017

Published in: Problems and Recent Methods in Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/conm/687/13733

zbMATH Keywords

positive coneMazur-Ulam theoremgyrogroupnormed gyrolinear spaces

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Normed linear spaces and Banach spaces; Banach lattices (46B99) General theory of (C^*)-algebras (46L05) Transformers, preservers (linear operators on spaces of linear operators) (47B49)

Cites Work

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• On the standard K-loop structure of positive invertible elements in a \(C^\ast\)-algebra
• Isometries of the unitary groups and Thompson isometries of the spaces of invertible positive elements in \(C^\ast\)-algebras
• Hyperbolic triangle centers. The special relativistic approach
• Generalized gyrovector spaces and a Mazur--Ulam theorem
• A Gyrovector Space Approach to Hyperbolic Geometry
• A Proof of the Mazur-Ulam Theorem
• Maps which preserve equality of distance
• Beyond the Einstein addition law and its gyroscopic Thomas precession. The theory of gyrogroups and gyrovector spaces

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