Jordan triple endomorphisms and isometries of unitary groups

DOI10.1016/j.laa.2013.09.013zbMath1285.15016OpenAlexW1981781849MaRDI QIDQ2435554

Lajos Molnár

Publication date: 19 February 2014

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

Full work available at URL: https://doi.org/10.1016/j.laa.2013.09.013

zbMATH Keywords

unitary grouplinear preserver problemisometriesunitarily invariant normJordan triple productJordan triple automorphism

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Algebraic systems of matrices (15A30) Linear preserver problems (15A86)

Related Items (13)

Continuous maps preserving Jordan triple products from \(\mathbb{U}_n\) to \(\mathbb{D}_m\) ⋮ Maps on the sphere of the algebras of matrices ⋮ Jordan triple homomorphisms on \(\mathcal{T}_{\infty} (F)\) ⋮ Surjective \(L^p\)-isometries on Grassmann spaces ⋮ Maps preserving products of commuting elements in von Neumann algebras ⋮ Bijections on the Unit Ball of $B(H)$ Preserving $^{\ast}$-Jordan Triple Product ⋮ Isometries of the geodesic distances for the space of invertible positive operators and matrices ⋮ A few conditions for a \(C^*\)-algebra to be commutative ⋮ Piecewise \(^\ast\)-homomorphisms and Jordan maps on \(C^\ast\)-algebras and factor von Neumann algebras ⋮ Additivity of quadratic maps on JB algebras ⋮ Generalized isometries of the special unitary group ⋮ Continuous maps preserving Jordan triple products from 𝔾𝕃₁to 𝔾𝕃₂and 𝔾𝕃₃ ⋮ The solution of Tingley's problem for the operator norm unit sphere of complex \(n\times n\) matrices

Cites Work

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• Isometries of the special orthogonal group
• Transformations of the unitary group on a Hilbert space
• A characterization of W*-algebras
• Selected preserver problems on algebraic structures of linear operators and on function spaces
• Linear maps preserving commutativity
• Isometries and maps compatible with inverted Jordan triple products on groups
• Optimal paths for symmetric actions in the unitary group
• Isometries of the unitary groups and Thompson isometries of the spaces of invertible positive elements in \(C^\ast\)-algebras
• Sequentially independent effects
• Induced metric and matrix inequalities on unitary matrices
• Metrics On Unitary Matrices And Their Application To Quantifying The Degree Of Non-Commutativity Between Unitary Matrices
• Introduction to Dynamical Systems

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