Affine geometric proofs of the Banach Stone theorems of Kadison and Kaup

DOI10.1216/rmjm/1181073116zbMath0738.47029OpenAlexW2087861319MaRDI QIDQ1173646

S. Singh

Publication date: 25 June 1992

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmjm/1181073116

zbMATH Keywords

\(JB^*\)-triplesstate spaceJordan isomorphisminfinite dimensional holomorphysurjective linear isometrybidualsBanach Stone theorem\(JB^*\)-triple isomorphismaffine geometric properties of facesextremal convex subsetsspectral, polar and Jordan decompositionstheorem of Effros

Mathematics Subject Classification ID

Spaces of vector- and operator-valued functions (46E40) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Linear operators in (C^*)- or von Neumann algebras (47C15)

Related Items (14)

Surjective isometries between unitary sets of unital JB\(^\ast \)-algebras ⋮ Similarities and differences between real and complex Banach spaces: an overview and recent developments ⋮ Isometries between \(C^ *\)-algebras. ⋮ Reflexivity of the group of surjective isometries on some Banach spaces ⋮ On real forms of JB\(^*\)-triples ⋮ Generalized bicircular projections on JB\(^*\)-triples ⋮ Geometric characterization of tripotents in real and complex JB\(^{*}\)-triples ⋮ Generalized 𝑛-circular projections on JB*-triples ⋮ Linear maps on the space of all bounded observables preserving maximal deviation. ⋮ On a Class of Projections on *-Rings ⋮ Orthogonal forms and orthogonality preservers on real function algebras ⋮ The structure of triple homomorphisms onto prime algebras ⋮ Linear rank and corank preserving maps on \({\mathcal B}(H)\) and an application to \(^*\)-semigroup isomorphisms of operator ideals ⋮ Reflexivity of the automorphism and isometry groups of the suspension of \({\mathcal B}({\mathcal H})\)

Cites Work

• Cônes autopolaires et algèbres de Jordan
• Solution of the contractive projection problem
• A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces
• Conditional expectation and bicontractive projections on Jordan \(C^ *\)- algebras and their generalizations
• The Gelfand-Naimark theorem for \(JB^ *\)-triples
• Algebraic characterization of symmetric complex Banach manifolds
• Jordan \(C^*\)-algebras
• A Gelfand-Neumark theorem for Jordan algebras
• Jordan algebras of type I
• Order ideals in a \(C^*\)-algebra and its dual
• Postulates for general quantum mechanics
• Isometries of operator algebras
• The multiplicative structure of 𝐽-contractive matrix functions
• Function Representation of Commutative Operator Triple Systems
• Weak*-continuity of Jordan triple products and its applications.
• On Isometries of Jordan Algebras
• On the ideal structure of operator algebras
• Jordan algebras of self-adjoint operators
• Irreducible Jordan Algebras of Self-Adjoint Operators
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