Description

Book Synopsis
Presents a systematic account of the developments in the theory of symmetric manifolds achieved over the past 50 years. The book contains detailed and friendly, but rigorous, proofs of the key results in the theory.

Table of Contents
  • JB$^*$-triples in dual Banach spaces
  • From bounded domains to symmetric Banach manifolds: Analytic manifolds and their automorphism groups
  • Uniform manifolds and their automorphism groups
  • The semigroup $\mathcal{O}_c(X)$ of holomorphic contractions
  • Manifolds with a compatible invariant metrics
  • Manifolds with a compatible tangent norm
  • Symmetric normed manifolds
  • J$^*$-triples and their related Lie algebras
  • The J$^*$-triple associated with a symmetric manifold
  • The symmetric manifold associated with a J$^*$-triple
  • Finite Rank J$^*$-triples and JH$^*$-triples: Algebraic study of J$^*$-triples
  • Atomic J$^*$-triples and JH$^*$-triples
  • From symmetric Banach manifolds to JB$^*$-triples: Spectral properties and bounded J$^*$-triples
  • The Riemann mapping theorem for JB$^*$-triples
  • The category of JB$^*$-triples
  • Automorphisms of bounded symmetric domains
  • Tripotents in JB$^*$-triples
  • Functional calculus in a JB$^*$-triple. Applications
  • Automorphisms of Banach-Grassmann manifolds
  • Symmetric Grassmann manifolds over Hilbert spaces
  • Affine structure of the unit ball in a JB$^*$-triple
  • JB$^*$-triples in dual Banach spaces or JBW$^*$-triples: Structure theory for JBW$^*$-triples and their preduals
  • Facial structure in JBW$^*$-triples and in JB$^*$-triples
  • The strong and strong* topologies in JBW$^*$-triples
  • Derivations of JB$^*$-triples
  • Some results on functional analysis
  • Lists of symbols and their meanings
  • Bibliography
  • Index.

    Jordan Triple Systems in Complex and Functional

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      A Hardback by Jose M. Isidro

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        View other formats and editions of Jordan Triple Systems in Complex and Functional by Jose M. Isidro

        Publisher: MP-AMM American Mathematical
        Publication Date: 1/30/2020 12:00:00 AM
        ISBN13: 9781470450830, 978-1470450830
        ISBN10: 1470450836

        Description

        Book Synopsis
        Presents a systematic account of the developments in the theory of symmetric manifolds achieved over the past 50 years. The book contains detailed and friendly, but rigorous, proofs of the key results in the theory.

        Table of Contents
        • JB$^*$-triples in dual Banach spaces
        • From bounded domains to symmetric Banach manifolds: Analytic manifolds and their automorphism groups
        • Uniform manifolds and their automorphism groups
        • The semigroup $\mathcal{O}_c(X)$ of holomorphic contractions
        • Manifolds with a compatible invariant metrics
        • Manifolds with a compatible tangent norm
        • Symmetric normed manifolds
        • J$^*$-triples and their related Lie algebras
        • The J$^*$-triple associated with a symmetric manifold
        • The symmetric manifold associated with a J$^*$-triple
        • Finite Rank J$^*$-triples and JH$^*$-triples: Algebraic study of J$^*$-triples
        • Atomic J$^*$-triples and JH$^*$-triples
        • From symmetric Banach manifolds to JB$^*$-triples: Spectral properties and bounded J$^*$-triples
        • The Riemann mapping theorem for JB$^*$-triples
        • The category of JB$^*$-triples
        • Automorphisms of bounded symmetric domains
        • Tripotents in JB$^*$-triples
        • Functional calculus in a JB$^*$-triple. Applications
        • Automorphisms of Banach-Grassmann manifolds
        • Symmetric Grassmann manifolds over Hilbert spaces
        • Affine structure of the unit ball in a JB$^*$-triple
        • JB$^*$-triples in dual Banach spaces or JBW$^*$-triples: Structure theory for JBW$^*$-triples and their preduals
        • Facial structure in JBW$^*$-triples and in JB$^*$-triples
        • The strong and strong* topologies in JBW$^*$-triples
        • Derivations of JB$^*$-triples
        • Some results on functional analysis
        • Lists of symbols and their meanings
        • Bibliography
        • Index.

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