Isometries of the special orthogonal group

DOI10.1016/j.laa.2013.03.008zbMath1297.47038OpenAlexW2062407529MaRDI QIDQ389604

Toshikazu Abe, Osamu Hatori, Shigeki Akiyama

Publication date: 21 January 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.2013.03.008

zbMATH Keywords

singular valuesspecial orthogonal groupisometriesspectrally multiplicative mappings

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Transformers, preservers (linear operators on spaces of linear operators) (47B49) Orthogonal matrices (15B10)

Related Items (10)

Continuous maps preserving Jordan triple products from \(\mathbb{U}_n\) to \(\mathbb{D}_m\) ⋮ Continuous maps preserving Jordan triple products from \(\mathbb{GL}_n(\mathbb{C})\) into \(\mathbb{C}^\ast\) ⋮ The full group of isometries of some compact Lie groups endowed with a bi-invariant metric ⋮ Jordan triple endomorphisms and isometries of unitary groups ⋮ On certain generalized isometries of the special orthogonal group ⋮ Tingley's problem on finite von Neumann algebras ⋮ Maps between Banach algebras preserving the spectrum ⋮ Continuous maps preserving Jordan triple products from 𝔾𝕃₁to 𝔾𝕃₂and 𝔾𝕃₃ ⋮ The operation $ABA$ in operator algebras ⋮ The solution of Tingley's problem for the operator norm unit sphere of complex \(n\times n\) matrices

Cites Work

• Determining elements in Banach algebras through spectral properties
• On the groups isomorphism of unitary groups in \(AW^*\)-algebras
• Duality between some linear preserver problems. III: c-spectral norms and (skew)-symmetric matrices with fixed singular values
• Isometries and maps compatible with inverted Jordan triple products on groups
• Isometries of the unitary groups and Thompson isometries of the spaces of invertible positive elements in \(C^\ast\)-algebras
• Some characterizations of the automorphisms of $B(H)$ and $C(X)$
• Isometries of the unitary group
• ON THE MAGIC MATRIX BY MAKHLIN AND THE B-C-H FORMULA IN SO(4)
• Introduction to Dynamical Systems
• Unnamed Item

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