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Full 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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. 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.
Contents
Volume 1non-associative Vidav-Palmer theorem; 3. Concluding the proof of the non-associative Vidav-Palmer theorem; 4. Jordan spectral theory; References; 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.
