Non-Associative Normed Algebras (Encyclopedia of Mathematics and its Applications)

Cabrera García, Miguel/ Rodríguez Palacios, Ángel

Cambridge University Press（2014/07発売）

• 製本 Hardcover:ハードカバー版／ページ数 733 p.
• 言語 ENG
• 商品コード 9781107043060
• DDC分類 512

Full Description

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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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

Contents

Preface; 1. Foundations; 2. Beginning the proof of the non-associative Vidav-Palmer theorem; 3. Concluding the proof of the non-associative Vidav-Palmer theorem; 4. Jordan spectral theory; References; Symbol index; Subject index.