Non-Associative Normed Algebras

Erscheinungsjahr 2018
ISBN: 978-1-107-04311-4
Verlag: Cambridge University Press

Buch, Englisch, Band 167, 754 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 1427 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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. 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.

Autoren/Hrsg.

Cabrera García, Miguel

Rodríguez Palacios, Ángel

Inhaltsverzeichnis

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.

Über Autor(innen)

Cabrera García, Miguel
Miguel Cabrera Garc?a 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
?el Rodr?guez 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.