Non-associative normed algebras: Vol 1 The Vidav-Palmer and Gelfand-Naimark theorems, Vol. 154
García, Miguel Cabrera
Non-associative normed algebras: Vol 1 The Vidav-Palmer and Gelfand-Naimark theorems, Vol. 154 - Cambridge: Cambridge University Press, 2014. - xxii; 712 p. Hb.; 24 cm. - Encyclopedia of mathematics and its applications .
Includes bibliographical references (pages 671-703) and indexes.
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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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.
9781107043060
Mathematics
Algebra
Intermediate.
Banach Algebras
512.554 / GAR
Non-associative normed algebras: Vol 1 The Vidav-Palmer and Gelfand-Naimark theorems, Vol. 154 - Cambridge: Cambridge University Press, 2014. - xxii; 712 p. Hb.; 24 cm. - Encyclopedia of mathematics and its applications .
Includes bibliographical references (pages 671-703) and indexes.
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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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.
9781107043060
Mathematics
Algebra
Intermediate.
Banach Algebras
512.554 / GAR
