Reflexivity of the group of surjective isometries on some Banach spaces

DOI10.1017/S0013091500019982zbMath0930.47015OpenAlexW2098136948MaRDI QIDQ4267543

Lajos Molnár, Borut Zalar

Publication date: 5 October 1999

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0013091500019982

zbMATH Keywords

isometry groupalgebraic reflexivityvon Neumann-Schatten \(p\)-classes of compact operators

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Isometric theory of Banach spaces (46B04) Transformers, preservers (linear operators on spaces of linear operators) (47B49)

Related Items (29)

Reflexivity of sets of isometries on bounded variation function spaces ⋮ Algebraic reflexivity of isometries on spaces of continuously differentiable functions ⋮ Isometries and approximate local isometries between \(\mathrm{AC}^p (X)\)-spaces ⋮ Local isometries on subspaces and subalgebras of function spaces ⋮ Approximate local isometries of Banach algebras of differentiable functions ⋮ On local isometries between algebras of \(C(Y)\)-valued differentiable maps ⋮ Local isometries on subspaces of continuous functions ⋮ Automorphisms of algebras of smooth functions and equivalent functions ⋮ Kakutani's automorphism theorem for vector-valued bounded holomorphic functions ⋮ A Survey on Isometries Between Lipschitz Spaces ⋮ Algebraic and topological reflexivity properties of \(l^p(X)\)spaces ⋮ Algebraic reflexivity of diameter-preserving linear bijections between \(C(X)\)-spaces ⋮ Algebraic reflexivity of isometry groups of algebras of Lipschitz maps ⋮ A note on the algebraic reflexivity of the group of surjective isometries of \(\mathcal K(C(K))\) ⋮ Some characterizations of the automorphisms of $B(H)$ and $C(X)$ ⋮ A SPHERICAL VERSION OF THE KOWALSKI–SŁODKOWSKI THEOREM AND ITS APPLICATIONS ⋮ Algebraic reflexivity of sets of bounded operators on vector valued Lipschitz functions ⋮ Algebraic reflexivity of the isometry group of some spaces of Lipschitz functions ⋮ Algebraic reflexivity of sets of bounded linear operators on absolutely continuous function spaces ⋮ Approximate local isometries on spaces of absolutely continuous functions ⋮ The Mazur–Ulam property for commutative von Neumann algebras ⋮ On 2-local diameter-preserving maps between \(C(X)\)-spaces ⋮ On 2-local isometries on continuous vector-valued function spaces ⋮ Generalized 2-local isometries of spaces of continuously differentiable functions ⋮ Some linear preserver problems on \(B(H)\) concerning rank and corank ⋮ Local isometries on spaces of continuous functions ⋮ Local and 2-local isometries between absolutely continuous function spaces ⋮ A new look at local maps on algebraic structures of matrices and operators ⋮ A reflexivity problem concerning the 𝐶*-algebra 𝐶(𝑋)⊗ℬ(ℋ)

Cites Work

• A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces
• Isometries of norm ideals of compact operators
• Affine geometric proofs of the Banach Stone theorems of Kadison and Kaup
• Characterizations of derivations on some normed algebras with involution
• The isometries of \(C_p\)
• Local derivations
• A note on unitary operators in \(C^ *\)-algebras
• Reflexivity, Algebraic Reflexivity and Linear Interpolation
• Mappings which Preserve Idempotents, Local Automorphisms, and Local Derivations
• On the Jordan Structure of C ∗ -Algebras

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