Isometries and maps compatible with inverted Jordan triple products on groups

DOI10.3836/tjm/1358951327zbMath1271.46010OpenAlexW2086580230MaRDI QIDQ1943244

Takeshi Miura, Go Hirasawa, Osamu Hatori, Lajos Molnár

Publication date: 19 March 2013

Published in: Tokyo Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.tjm/1358951327

zbMATH Keywords

unitary groupsMazur-Ulam theorem\(d\)-preserving mapsgroups in function spacesisometries on groupsmetric spaces of positive invertible elements in \(C^\ast\)-algebras

Mathematics Subject Classification ID

Banach algebras of continuous functions, function algebras (46J10) Isometric theory of Banach spaces (46B04) Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups (20K30)

Related Items (18)

Surjective isometries between unitary sets of unital JB\(^\ast \)-algebras ⋮ Isometries of the unitary group ⋮ Continuous maps preserving Jordan triple products from \(\mathbb{U}_n\) to \(\mathbb{D}_m\) ⋮ Jordan triple endomorphisms and isometries of spaces of positive definite matrices ⋮ Continuous maps preserving Jordan triple products from \(\mathbb{GL}_n(\mathbb{C})\) into \(\mathbb{C}^\ast\) ⋮ Isometries of the special orthogonal group ⋮ Can one identify two unital JB*-algebras by the metric spaces determined by their sets of unitaries? ⋮ Spectral conditions for Jordan *-isomorphisms on operator algebras ⋮ Surjective \(L^p\)-isometries on Grassmann spaces ⋮ Jordan triple endomorphisms and isometries of unitary groups ⋮ Surjective isometries on Grassmann spaces ⋮ Isometries of the geodesic distances for the space of invertible positive operators and matrices ⋮ Transformations on positive definite matrices preserving generalized distance measures ⋮ Transformations of the unitary group on a Hilbert space ⋮ 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 ⋮ Continuous maps preserving Jordan triple products from 𝔾𝕃₁to 𝔾𝕃₂and 𝔾𝕃₃ ⋮ Maps which preserve norms of non-symmetrical quotients between groups of exponentials of Lipschitz functions

Cites Work

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• Reflections and a generalization of the Mazur-Ulam theorem
• Algebraic properties of isometries between groups of invertible elements in Banach algebras
• Divisibly norm-preserving maps between commutative Banach algebras
• On the groups isomorphism of unitary groups in \(AW^*\)-algebras
• Isometries of the unitary group
• Isometries between groups of invertible elements in Banach algebras
• Thompson isometries on positive operators: The 2-dimensional case
• Thompson isometries of the space of invertible positive operators
• A Proof of the Mazur-Ulam Theorem
• Maps which preserve equality of distance

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