Author: Miguel Cabrera García Publisher: Cambridge University Press ISBN: 1139992775 Category : Mathematics Languages : en Pages : 735
Book 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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. 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.
Author: Miguel Cabrera García Publisher: ISBN: 9781316004302 Category : MATHEMATICS Languages : en Pages : 736
Book Description
The first systematic account of the basic theory of normed algebras, without assuming associativity. Sure to become a central resource.
Author: Miguel Cabrera García Publisher: ISBN: Category : Algebra Languages : en Pages : 0
Book 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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. 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 Publisher's note.
Author: Miguel Cabrera García Publisher: Cambridge University Press ISBN: 1108570763 Category : Mathematics Languages : en Pages : 759
Book 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. 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.
Author: Miguel Cabrera García Publisher: Cambridge University Press ISBN: 1107043115 Category : Mathematics Languages : en Pages : 759
Book Description
The first systematic account of the basic theory of normed algebras, without assuming associativity. Sure to become a central resource.
Author: Abdenacer Makhlouf Publisher: John Wiley & Sons ISBN: 1789450179 Category : Mathematics Languages : en Pages : 370
Book Description
This book is part of Algebra and Geometry, a subject within the SCIENCES collection published by ISTE and Wiley, and the first of three volumes specifically focusing on algebra and its applications. Algebra and Applications 1 centers on non-associative algebras and includes an introduction to derived categories. The chapters are written by recognized experts in the field, providing insight into new trends, as well as a comprehensive introduction to the theory. The book incorporates self-contained surveys with the main results, applications and perspectives. The chapters in this volume cover a wide variety of algebraic structures and their related topics. Jordan superalgebras, Lie algebras, composition algebras, graded division algebras, non-associative C*- algebras, H*-algebras, Krichever-Novikov type algebras, preLie algebras and related structures, geometric structures on 3-Lie algebras and derived categories are all explored. Algebra and Applications 1 is of great interest to graduate students and researchers. Each chapter combines some of the features of both a graduate level textbook and of research level surveys.
Author: Mercedes Siles Molina Publisher: Springer Nature ISBN: 3030352560 Category : Mathematics Languages : en Pages : 338
Book Description
This book gathers together selected contributions presented at the 3rd Moroccan Andalusian Meeting on Algebras and their Applications, held in Chefchaouen, Morocco, April 12-14, 2018, and which reflects the mathematical collaboration between south European and north African countries, mainly France, Spain, Morocco, Tunisia and Senegal. The book is divided in three parts and features contributions from the following fields: algebraic and analytic methods in associative and non-associative structures; homological and categorical methods in algebra; and history of mathematics. Covering topics such as rings and algebras, representation theory, number theory, operator algebras, category theory, group theory and information theory, it opens up new avenues of study for graduate students and young researchers. The findings presented also appeal to anyone interested in the fields of algebra and mathematical analysis.
Author: Gilles Godefroy Publisher: American Mathematical Society ISBN: 1470475707 Category : Mathematics Languages : en Pages : 358
Book Description
This book provides a comprehensive presentation of recent approaches to and results about properties of various classes of functional spaces, such as Banach spaces, uniformly convex spaces, function spaces, and Banach algebras. Each of the 12 articles in this book gives a broad overview of current subjects and presents open problems. Each article includes an extensive bibliography. This book is dedicated to Professor Per. H. Enflo, who made significant contributions to functional analysis and operator theory.
Author: José M. Isidro Publisher: American Mathematical Soc. ISBN: 1470450836 Category : Education Languages : en Pages : 560
Book Description
This book is a systematic account of the impressive developments in the theory of symmetric manifolds achieved over the past 50 years. It contains detailed and friendly, but rigorous, proofs of the key results in the theory. Milestones are the study of the group of holomomorphic automorphisms of bounded domains in a complex Banach space (Vigué and Upmeier in the late 1970s), Kaup's theorem on the equivalence of the categories of symmetric Banach manifolds and that of hermitian Jordan triple systems, and the culminating point in the process: the Riemann mapping theorem for complex Banach spaces (Kaup, 1982). This led to the introduction of wide classes of Banach spaces known as JB∗-triples and JBW∗-triples whose geometry has been thoroughly studied by several outstanding mathematicians in the late 1980s. The book presents a good example of fruitful interaction between different branches of mathematics, making it attractive for mathematicians interested in various fields such as algebra, differential geometry and, of course, complex and functional analysis.
Author: Miguel Cabrera García
Author: Miguel Cabrera García
Author: Miguel Cabrera García
Author: Miguel Cabrera García
Author: Miguel Cabrera García
Author: Miguel Cabrera García
Author: Abdenacer Makhlouf
Author: Mercedes Siles Molina
Author: Gilles Godefroy
Author: José M. Isidro