Jordan triple endomorphisms and isometries of spaces of positive definite matrices
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Publication:2938315
DOI10.1080/03081087.2013.844231zbMath1310.15062OpenAlexW2004335786MaRDI QIDQ2938315
Publication date: 14 January 2015
Published in: Linear and Multilinear Algebra (Search for Journal in Brave)
Full work available at URL: http://real.mtak.hu/9206/1/M_LAMA.pdf
positive definite matricesisometriesunitarily invariant normsJordan triple endomorphismsgeodesic distancesymmetric Stein divergence
Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Positive matrices and their generalizations; cones of matrices (15B48)
Related Items (13)
On the surjectivity of generalized isometries on the positive definite cone of matrices ⋮ The arithmetic, geometric and harmonic means in operator algebras and transformations among them ⋮ Applications of the automatic additivity of positive homogeneous order isomorphisms between positive definite cones in \(C^*\)-algebras ⋮ Maps preserving products of commuting elements in von Neumann algebras ⋮ Unnamed Item ⋮ A few conditions for a \(C^*\)-algebra to be commutative ⋮ Preserving problems of geodesic-affine maps and related topics on positive definite matrices ⋮ Examples and applications of generalized gyrovector spaces ⋮ Piecewise \(^\ast\)-homomorphisms and Jordan maps on \(C^\ast\)-algebras and factor von Neumann algebras ⋮ Elliptic isometries of the manifold of positive definite real matrices with the trace metric ⋮ Additivity of quadratic maps on JB algebras ⋮ Maps on positive definite matrices preserving Bregman and Jensen divergences ⋮ Continuous Jordan triple endomorphisms of \(\mathbb{P}_2\)
Cites Work
- Riemannian geometry and matrix geometric means
- Selected preserver problems on algebraic structures of linear operators and on function spaces
- Some aspects of the theory of norms
- Linear maps preserving commutativity
- Isometries and maps compatible with inverted Jordan triple products on groups
- Differential and metrical structure of positive operators
- Isometries of the unitary groups and Thompson isometries of the spaces of invertible positive elements in \(C^\ast\)-algebras
- Means of Hermitian positive-definite matrices based on the log-determinant \(\alpha\)-divergence function
- Sequentially independent effects
- Isometries of the unitary group
- GEODESICS AND OPERATOR MEANS IN THE SPACE OF POSITIVE OPERATORS
- Linear operators preserving unitary similarity invariant norms
- Thompson isometries of the space of invertible positive operators
- Isometries of symmetric gauge functions
- Non-linear Jordan triple automorphisms of sets of self-adjoint matrices and operators
- A remark on the Kochen-Specker theorem and some characterizations of the determinant on sets of Hermitian matrices
- Operator differentiable functions
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