Miguel Cabrera Garcia

Non-Associative Normed Algebras : Volume 2, Representation Theory and the Zel'manov Approach (eBook, PDF)

• Format: PDF

Produktbeschreibung

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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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 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. This completes the work begun in the first volume, which introduced these algebras and discussed the so-called non-associative Gelfand-Naimark and Vidav-Palmer theorems. This book interweaves pure algebra, geometry of normed spaces, and infinite-dimensional complex analysis. Novel proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, and an extensive bibliography.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 12. April 2018
• Englisch
• ISBN-13: 9781108631433
• Artikelnr.: 53399571

Autorenporträt

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.

Inhaltsangabe

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
Bibliography of Volume 1
Additional bibliography to Volume 2
Symbol index for Volume 1
Subject index for Volume 1
Symbol index for Volume 2
Subject index for Volume 2.