Non-Associative Normed Algebras: Volume 2 (Encyclopedia of Mathematics and its Applications)
Cambridge University Press, 4/12/2018
EAN 9781107043114, ISBN10: 1107043115
Hardcover, 754 pages, 24 x 16 x 4.6 cm
Language: English
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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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.
Preface
5. Non-commutative JBW*-algebras, JB*-triples revisited, and a unit-free Vidav–Palmer type non-associative theorem
6. Representation theory for non-commutative JB*-algebras and alternative C*-algebras
7. Zel'manov approach
8. Selected topics in the theory of non-associative normed algebras
Bibliography of Volume 1
Additional bibliography to Volume 2
Symbol index for Volume 1
Subject index for Volume 1
Symbol index for Volume 2
Subject index for Volume 2.