TY  - GEN
AU  - García, Miguel Cabrera
AU  - Palacios, Ángel Rodríguez 
TI  - Non-associative normed algebras: Vol 1 The Vidav-Palmer and Gelfand-Naimark theorems, Vol. 154
SN  - 9781107043060
U1  - 512.554 
PY  - 2014///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Mathematics
KW  - Algebra
KW  - Intermediate
KW  - Banach Algebras
N1  - Includes bibliographical references (pages 671-703) and indexes
N2  - 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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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 first volume focuses on the non-associative generalizations of (associative) C*-algebras provided by the so-called non-associative Gelfand–Naimark and Vidav–Palmer theorems, which give rise to alternative C*-algebras and non-commutative JB*-algebras, respectively. The relationship between non-commutative JB*-algebras and JB*-triples is also fully discussed. The second volume covers Zel'manov's celebrated work in Jordan theory to derive classification theorems for non-commutative JB*-algebras and JB*-triples, as well as other topics. The book interweaves pure algebra, geometry of normed spaces, and complex analysis, and includes a wealth of historical comments, background material, examples and exercises. The authors also provide an extensive bibliography
ER  -