Jordan Triple Systems in Complex and Functional Analysis by J... - 9781470450830

Jordan Triple Systems in Complex and Functional AnalysisAuthor(s): Jose M. Isidro\nFormat: Hardback\nPublisher: American Mathematical Society, United States\nImprint: American Mathematical Society\nISBN-13: 9781470450830, 978-1470450830\nSynopsis\nThis 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 geometr.