Non-associative normed algebras. Volume 2, Representation theory and the Zel'manov approach / Miguel Cabrera García, Ángel Rodríguez Palacios.

Format:

Book

Author/Creator:

Cabrera García, Miguel, author.

Rodríguez Palacios, Ángel, author.

Series:

Encyclopedia of mathematics and its applications ; 167.

Encyclopedia of mathematics and its applications ; 167

Language:

English

Subjects (All):

Banach algebras.

Algebra.

Physical Description:

1 online resource (xxvii, 729 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2018.

Summary:

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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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

Notes:

Title from publisher's bibliographic system (viewed on 24 Apr 2018).

ISBN:

1-108-57076-3

1-107-33781-X

1-108-63143-6