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Non-associative normed algebras.Volu...

Cabrera Garcia, Miguel.

Non-associative normed algebras.Volume 1,The Vidav-Palmer and Gelfand-Naimark theorems

Record Type:	Electronic resources : Monograph/item
Title/Author:	Non-associative normed algebras.Miguel Cabrera Garcia, Angel Rodriguez Palacios.
remainder title:	The Vidav-Palmer and Gelfand-Naimark theorems
Author:	Cabrera Garcia, Miguel.
other author:	Rodriguez Palacios, Angel.
Published:	Cambridge :Cambridge University Press,2014.
Description:	xxii, 712 p. :ill., digital ;24 cm.
Subject:	Banach algebras.
Online resource:	https://doi.org/10.1017/CBO9781107337763
ISBN:	9781107337763$q(electronic bk.)

Non-associative normed algebras.Volume 1,The Vidav-Palmer and Gelfand-Naimark theorems
Cabrera Garcia, Miguel.

Non-associative normed algebras.Volume 1,The Vidav-Palmer and Gelfand-Naimark theorems[electronic resource] /The Vidav-Palmer and Gelfand-Naimark theoremsMiguel Cabrera Garcia, Angel Rodriguez Palacios. - Cambridge :Cambridge University Press,2014. - xxii, 712 p. :ill., digital ;24 cm. - Encyclopedia of mathematics and its applications ;154. - Encyclopedia of mathematics and its applications ;v. 124-125..

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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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

ISBN: 9781107337763$q(electronic bk.)Subjects--Topical Terms:

247399
Banach algebras.

LC Class. No.: QA326 / .C33 2014

Dewey Class. No.: 512.554

Non-associative normed algebras.Volume 1,The Vidav-Palmer and Gelfand-Naimark theorems
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520 $a 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.
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