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Non-Associative Normed Algebras

Non-Associative Normed Algebras
2 Volume Hardback Set

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: May 2018
  • availability: Temporarily unavailable - available from TBC
  • format: Multiple copy pack
  • isbn: 9781108679077

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About the Authors
  • 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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. The 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 revisits JB*-triples, covers Zel'manov's celebrated work in Jordan theory, proves the unit-free variant of the Vidav–Palmer theorem, and develops the representation theory of alternative C*-algebras and non-commutative JB*-algebras. 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.

    • Brings together research previously scattered across many different papers and books
    • Authors are both leading experts in the field
    • Unique resource for students and researchers in the field
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    Product details

    • Date Published: May 2018
    • format: Multiple copy pack
    • isbn: 9781108679077
    • length: 1494 pages
    • dimensions: 241 x 165 x 85 mm
    • weight: 2.44kg
    • availability: Temporarily unavailable - available from TBC
  • Table of Contents

    Volume 1: 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
    Symbol index
    Subject index. Volume 2: Preface
    5. Non-commutative JBW*-algebras, JB*-triples revisited, and a unit-free Vidav–Palmer type non-associative theorem
    6. Representation theory for non-commutative JB*-algebras and alternative C*-algebras
    7. Zel'manov approach
    8. Selected topics in the theory of non-associative normed algebras
    Reference – Papers
    References – Books
    Symbol index for Volume 2
    Subject index for Volume 2
    Symbol index for Volume 1
    Subject index for Volume 1.

  • Resources for

    Non-Associative Normed Algebras

    Miguel Cabrera García, Ángel Rodríguez Palacios

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  • Authors

    Miguel Cabrera García, Universidad de Granada
    Miguel Cabrera García is a Professor in the Department of Mathematical Analysis at the University of Granada, Spain. He is a leading expert in non-associative normed algebras and multiplication algebras, and has collaborated with outstanding mathematicians, including M. Bresar, W. S. Martindale III, and E. I. Zel'manov.

    Ángel Rodríguez Palacios, Universidad de Granada
    Ángel Rodríguez Palacios is a Professor in the Department of Mathematical Analysis at the University of Granada, Spain. He is regarded as the world leader in non-associative normed algebras, and has written more than 150 research papers on normed spaces and associative and non-associative normed algebras. Some of these papers have been written in collaboration with others, including C. H. Chu, H. G. Dales, W. Kaup, M. Neumann, A. M. Slin'ko, D. Yost, G. V. Wood, and E. I. Zel'manov.

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