Jordan Triple Systems in Complex and Functional Analysis

Jose M. Isidro, University of Santiago de Compestela, Santiago de Composetla, Galicia, Spain.

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.