Non-Associative Normed Algebras 2 Volume Hardback Set

Erscheinungsjahr 2018
ISBN: 978-1-108-67907-7
Verlag: Cambridge University Press

Buch, Englisch, 1494 Seiten, Format (B × H): 162 mm x 240 mm, Gewicht: 2495 g

Reihe: Encyclopedia of Mathematics and its Applications

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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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.

Autoren/Hrsg.

Cabrera García, Miguel

Rodríguez Palacios, Ángel

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Algebra

Inhaltsverzeichnis

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; 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.

Über Autor(innen)

Cabrera García, Miguel
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.

Rodríguez Palacios, Ángel
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.