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  3. Non-Associative Normed Algebras
  • Cited by 38
      • Volume 1: The Vidav–Palmer and Gelfand–Naimark Theorems
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    • Publisher:
      Cambridge University Press
      Publication date:
      05 August 2014
      31 July 2014
      ISBN:
      9781107337763
      9781107043060
      DOI:
      https://doi.org/10.1017/CBO9781107337763
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      1.23kg, 733 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis, Algebra
      Series:
      Encyclopedia of Mathematics and its Applications (154)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis, Algebra
    Series:
    Encyclopedia of Mathematics and its Applications (154)
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    Book 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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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.

    Reviews

    '… an impressive piece of work written by two experts in the theory of normed algebras whose multiplication may not be associative … This review is certainly too brief to do justice to the rich contents of this book, which is a welcome addition to the literature on functional analysis and is definitely useful to anyone with an interest in this area and related topics, ranging from beginner operator theorists to people interested in specific problems involving non-associative algebras.'

    Daniel Beltita Source: Mathematical Reviews

    'I dare say that this book is the first detailed treatise whose primary goal is the study of normed nonassociative algebras. The two authors are recognized experts in this topic, which combines functional analysis, geometry of Banach spaces and what could be called structure theory of algebras which are nearly associative.'

    Antonio Fernández López Source: zbMATH (www.zbmath.org)

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