Non-Associative Normed Algebras
Seiten
2014
Cambridge University Press (Verlag)
978-1-107-04306-0 (ISBN)
Cambridge University Press (Verlag)
978-1-107-04306-0 (ISBN)
The first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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 first volume of two focuses on C*-algebras and related structure.
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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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 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 covers Zel'manov's celebrated work in Jordan theory to derive classification theorems for non-commutative JB*-algebras and JB*-triples, as well as other topics. 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.
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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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 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 covers Zel'manov's celebrated work in Jordan theory to derive classification theorems for non-commutative JB*-algebras and JB*-triples, as well as other topics. 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.
Miguel Cabrera García is Professor in the Department of Mathematical Analysis at the University of Granada, Spain. Ángel Rodríguez Palacios is Professor in the Department of Mathematical Analysis at the University of Granada, Spain.
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.
| Reihe/Serie | Non-Associative Normed Algebras 2 Volume Hardback Set ; Volume 1 |
|---|---|
| Zusatzinfo | Worked examples or Exercises; 3 Line drawings, unspecified |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 159 x 240 mm |
| Gewicht | 1230 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| ISBN-10 | 1-107-04306-9 / 1107043069 |
| ISBN-13 | 978-1-107-04306-0 / 9781107043060 |
| Zustand | Neuware |
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