Generalized gyrovector spaces and a Mazur--Ulam theorem

DOI10.5486/PMD.2015.7234zbMath1374.46026OpenAlexW2626957552MaRDI QIDQ2973140

Osamu Hatori, Toshikazu Abe

Publication date: 31 March 2017

Published in: Publicationes Mathematicae Debrecen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.5486/pmd.2015.7234

zbMATH Keywords

gyrovector spacesMazur-Ulam theorem

Mathematics Subject Classification ID

Normed linear spaces and Banach spaces; Banach lattices (46B99) Loops, quasigroups (20N05)

Related Items (15)

On a notion of complex Möbius gyrovector spaces ⋮ Cardinal invariants in the quotient spaces of weakly topological groups ⋮ On a characterization of commutativity for {\(C^*\)}-algebras via gyrogroup operations ⋮ A Mazur-Ulam theorem for normed gyrolinear spaces ⋮ Extension of isometries in generalized gyrovector spaces of the positive cones ⋮ Orthogonal gyroexpansion in Möbius gyrovector spaces ⋮ The first-countability in the quotient spaces of topological gyrogroups ⋮ On Metric Structures of Normed Gyrogroups ⋮ Uniformities on strongly topological gyrogroups ⋮ Finitely generated gyrovector subspaces and orthogonal gyrodecomposition in the Möbius gyrovector space ⋮ Examples and applications of generalized gyrovector spaces ⋮ Involutive groups, unique 2-divisibility, and related gyrogroup structures ⋮ Algebraic structures for means ⋮ Continuous quasi gyrolinear functionals on Möbius gyrovector spaces ⋮ Extensions of some topological properties in topological gyrogroups

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