(Ebook) Non-Associative Normed Algebras. Volume 2: Representation Theory and the Zel’manov Approach by Miguel Cabrera García, Ángel Rodríguez Palacios ISBN 9781107043060, 9781107043114, 9781107337817, 9781108679077, 1107043069, 1107043115, 110733781X, 1108679072, B07B7M66KC

(Ebook) Non-Associative Normed Algebras. Volume 2: Representation Theory and the Zel’manov Approach by Miguel Cabrera García, Ángel Rodríguez Palacios ISBN 9781107043060, 9781107043114, 9781107337817, 9781108679077, 1107043069, 1107043115, 110733781X, 1108679072, B07B7M66KC

This first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.This second volume revisits JB*-triples, covers Zel'manov's celebrated work in Jordan theory, proves the unit-free variant of the Vidav–Palmer theorem, and develops the representation theory of alternative C*-algebras and non-commutative JB*-algebras. This completes the work begun in the first volume, which introduced these algebras and discussed the so-called non-associative Gelfand–Naimark and Vidav–Palmer theorems.This book interweaves pure algebra, geometry of normed spaces, and infinite-dimensional complex analysis. Novel proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, and an extensive bibliography.