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

• 作者： Cabrera Garcia, Miguel, author.
• 其他作者：
  • Rodriguez Palacios, Angel, author.
• 其他題名：
  • The Vidav-Palmer and Gelfand-Naimark theorems
  • Encyclopedia of mathematics and its applications ;
• 出版： Cambridge : Cambridge University Press
• 叢書名： Encyclopedia of mathematics and its applications ;154
• 主題： Banach algebras. , Algebra.
• ISBN： 9781107337763 (electronic bk.) 、 9781107043060 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
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• 摘要註: 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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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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