Non-Associative Normed Algebras : Volume 2, Representation Theory and the Zel'manov Approach

by Miguel Cabrera García & Ángel Rodríguez Palacios
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Publisher: Cambridge University Press

Series: Encyclopedia of Mathematics and its Applications

Publication Date: March 31, 2018

ISBN: 9781108570763

Binding: Kobo eBook

Availability: eBook

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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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