Jordan triple systems in complex and functional analysis
 Responsibility
 José M. Isidro
 Publication
 [Providence, Rhode Island] : American Mathematical Society, [2019]
 Copyright notice
 ©2019
 Physical description
 xiii, 560 pages ; 26 cm
 Series
 Mathematical surveys and monographs ; no. 243.
At the library
Science Library (Li and Ma)
Stacks
Call number  Status 

QA3 .A4 V.243  New books shelf Request 
More options
Description
Creators/Contributors
 Author/Creator
 Isidro, José M., author.
 Contributor
 Real Sociedad Matemática Española.
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 547556) and index
 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 BanachGrassmann 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.
 (source: Nielsen Book Data)
 Summary

This book is a systematic account of the impressive developments in the theory of symmetric manifolds achieved over the past 50 years. It contains detailed and friendly, but rigorous, proofs of the key results in the theory. Milestones are the study of the group of holomomorphic automorphisms of bounded domains in a complex Banach space (Vigue and Upmeier in the late 1970s), Kaup's theorem on the equivalence of the categories of symmetric Banach manifolds and that of hermitian Jordan triple systems, and the culminating point in the process: the Riemann mapping theorem for complex Banach spaces (Kaup, 1982). This led to the introduction of wide classes of Banach spaces known as $\mathrm{JB}^*$triples and $\mathrm{JBW}^*$triples whose geometry has been thoroughly studied by several outstanding mathematicians in the late 1980s. The book presents a good example of fruitful interaction between different branches of mathematics, making it attractive for mathematicians interested in various fields such as algebra, differential geometry and, of course, complex and functional analysis. This book is published in cooperation with Real Sociedad Matematica Espanola.
(source: Nielsen Book Data)
Subjects
 Subject
 Jordan algebras.
 Lie algebras.
 Hermitian symmetric spaces.
 Functional analysis.
 Functional analysis.
 Hermitian symmetric spaces.
 Jordan algebras.
 Lie algebras.
 Functional analysis  Measures, integration, derivative, holomorphy (all involving infinitedimensional spaces)  Infinitedimensional holomorphy.
 Global analysis, analysis on manifolds  Infinitedimensional manifolds  Questions of holomorphy.
 Differential geometry  Global differential geometry  Symmetric spaces.
 Several complex variables and analytic spaces  Complex spaces with a group of automorphisms  Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras.
 Nonassociative rings and algebras  Jordan algebras (algebras, triples and pairs)  Jordan structures on Banach spaces and algebras.
 Manifolds and cell complexes  Topological transformation groups  Noncompact Lie groups of transformations.
 Topological groups, Lie groups  Lie groups  Infinitedimensional Lie groups and their Lie algebras: general properties.
 Nonassociative rings and algebras  Lie algebras and Lie superalgebras  Infinitedimensional Lie (super)algebras.
 Functional analysis  Normed linear spaces and Banach spaces; Banach lattices  Geometry and structure of normed linear spaces.
 Global analysis, analysis on manifolds  Infinitedimensional manifolds  Group structures and generalizations on infinitedimensional manifolds.
Bibliographic information
 Publication date
 2019
 Copyright date
 2019
 Series
 Mathematical surveys and monographs ; volume 243
 Note
 "Real Sociedad Mathematica Espanola, Madrid, Spain."
 ISBN
 9781470450830 (alk. paper)
 1470450836 (alk. paper)