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Non-Associative Normed Algebras

Miguel Cabrera GarcíaÁngel Rodríguez Palacios

出版	Cambridge University Press, 2014-07-31
主題	Mathematics / GeneralMathematics / Algebra / GeneralMathematics / Algebra / AbstractMathematics / Algebra / LinearMathematics / Topology
ISBN	11070430699781107043060
URL	http://books.google.com.hk/books?id=Ri0DBAAAQBAJ&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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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.