Non-associative normed algebras. [E-Book] / Miguel Cabrera García, Ángel Rodríguez Palacios. Volume 2, Representation theory and the Zel'manov approach
Cabrera García, Miguel, (author)
Rodríguez Palacios, Ángel, (author)
Cambridge : Cambridge University Press, 2018
1 online resource (xxvii, 729 pages)
Encyclopedia of mathematics and its applications ; 167
Full Text
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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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.