Non-Associative Normed Algebras

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first systematic account of the basic theory of normed algebras without assuming associativity includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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.