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Non-Associative Normed Algebras

Miguel Cabrera GarcíaÁngel Rodríguez Palacios

出版	Cambridge University Press, 2018-04-12
主題	Mathematics / Algebra / GeneralMathematics / Algebra / AbstractMathematics / Algebra / LinearMathematics / Functional AnalysisMathematics / Topology
ISBN	11070431159781107043114
URL	http://books.google.com.hk/books?id=KEFPDwAAQBAJ&hl=&source=gbs_api
EBook	SAMPLE

註釋

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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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. Miguel Cabrera García is Professor in the Department of Mathematical Analysis at the University of Granada, Spain. Ángel Rodríguez Palacios is Professor in the Department of Mathematical Analysis at the University of Granada, Spain Publisher's note.