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Author : Bingren Li
Publisher : World Scientific
Page : 264 pages
File Size : 26,78 MB
Release : 2003
Category : Mathematics
ISBN : 9789812795182
Since the treatment is from the beginning (real Banach and Hilbert spaces, real Banach algebras,
Author : Bingren Li
Publisher : World Scientific
Page : 256 pages
File Size : 20,95 MB
Release : 2003-05-28
Category : Mathematics
ISBN : 981448590X
The theory of operator algebras is generally considered over the field of complex numbers and in the complex Hilbert spaces. So it is a natural and interesting problem: How is the theory in the field of real numbers? Up to now, the theory of operator algebras over the field of real numbers has seemed not to be introduced systematically and sufficiently.The aim of this book is to set up the fundamentals of real operator algebras and to give a systematic discussion for real operator algebras. Since the treatment is from the beginning (real Banach and Hilbert spaces, real Banach algebras, real Banach ∗ algebras, real C∗-algebras and W∗-algebras, etc.), and some basic facts are given, one can get some results on real operator algebras easily.The book is also an introduction to real operator algebras, written in a self-contained manner. The reader needs just a general knowledge of Banach algebras and operator algebras.
Author : Kehe Zhu
Publisher : CRC Press
Page : 172 pages
File Size : 35,38 MB
Release : 1993-05-27
Category : Mathematics
ISBN : 9780849378751
An Introduction to Operator Algebras is a concise text/reference that focuses on the fundamental results in operator algebras. Results discussed include Gelfand's representation of commutative C*-algebras, the GNS construction, the spectral theorem, polar decomposition, von Neumann's double commutant theorem, Kaplansky's density theorem, the (continuous, Borel, and L8) functional calculus for normal operators, and type decomposition for von Neumann algebras. Exercises are provided after each chapter.
Author : Masamichi Takesaki
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 25,13 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461261880
Mathematics for infinite dimensional objects is becoming more and more important today both in theory and application. Rings of operators, renamed von Neumann algebras by J. Dixmier, were first introduced by J. von Neumann fifty years ago, 1929, in [254] with his grand aim of giving a sound founda tion to mathematical sciences of infinite nature. J. von Neumann and his collaborator F. J. Murray laid down the foundation for this new field of mathematics, operator algebras, in a series of papers, [240], [241], [242], [257] and [259], during the period of the 1930s and early in the 1940s. In the introduction to this series of investigations, they stated Their solution 1 {to the problems of understanding rings of operators) seems to be essential for the further advance of abstract operator theory in Hilbert space under several aspects. First, the formal calculus with operator-rings leads to them. Second, our attempts to generalize the theory of unitary group-representations essentially beyond their classical frame have always been blocked by the unsolved questions connected with these problems. Third, various aspects of the quantum mechanical formalism suggest strongly the elucidation of this subject. Fourth, the knowledge obtained in these investigations gives an approach to a class of abstract algebras without a finite basis, which seems to differ essentially from all types hitherto investigated. Since then there has appeared a large volume of literature, and a great deal of progress has been achieved by many mathematicians.
Author : Bruce Blackadar
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 40,59 MB
Release : 2006-03-09
Category : Mathematics
ISBN : 3540285172
This book offers a comprehensive introduction to the general theory of C*-algebras and von Neumann algebras. Beginning with the basics, the theory is developed through such topics as tensor products, nuclearity and exactness, crossed products, K-theory, and quasidiagonality. The presentation carefully and precisely explains the main features of each part of the theory of operator algebras; most important arguments are at least outlined and many are presented in full detail.
Author : Erik M. Alfsen
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 45,26 MB
Release : 2001-04-27
Category : Mathematics
ISBN : 9780817638900
The topic of this book is the theory of state spaces of operator algebras and their geometry. The states are of interest because they determine representations of the algebra, and its algebraic structure is in an intriguing and fascinating fashion encoded in the geometry of the state space. From the beginning the theory of operator algebras was motivated by applications to physics, but recently it has found unexpected new applica tions to various fields of pure mathematics, like foliations and knot theory, and (in the Jordan algebra case) also to Banach manifolds and infinite di mensional holomorphy. This makes it a relevant field of study for readers with diverse backgrounds and interests. Therefore this book is not intended solely for specialists in operator algebras, but also for graduate students and mathematicians in other fields who want to learn the subject. We assume that the reader starts out with only the basic knowledge taught in standard graduate courses in real and complex variables, measure theory and functional analysis. We have given complete proofs of basic results on operator algebras, so that no previous knowledge in this field is needed. For discussion of some topics, more advanced prerequisites are needed. Here we have included all necessary definitions and statements of results, but in some cases proofs are referred to standard texts. In those cases we have tried to give references to material that can be read and understood easily in the context of our book.
Author : Bing-Ren Li
Publisher : World Scientific
Page : 758 pages
File Size : 32,71 MB
Release : 1992
Category : Mathematics
ISBN : 9789810209414
This book is an introductory text on one of the most important fields of Mathematics, the theory of operator algebras. It offers a readable exposition of the basic concepts, techniques, structures and important results of operator algebras. Written in a self-contained manner, with an emphasis on understanding, it serves as an ideal text for graduate students.
Author : Herbert Schröder
Publisher : Chapman and Hall/CRC
Page : 184 pages
File Size : 45,99 MB
Release : 1993-08-23
Category : Mathematics
ISBN :
This Research Note presents the K-theory and KK-theory for real C*-algebras and shows that these can be successfully applied to solve some topological problems which are not accessible to the tools developed in the complex setting alone.
Author : Liming Ge
Publisher : American Mathematical Soc.
Page : 416 pages
File Size : 50,20 MB
Release : 1998
Category : Mathematics
ISBN : 0821810936
This volume contains the proceedings from the International Conference on Operator Algebras and Operator Theory held at the East China Normal University in Shanghai (China). Participants in the conference ranged from graduate students to postdocs to leading experts who came from around the world. Topics covered were $C*$-algebras, von Neumann algebras, non-self-adjoint operator algebras, wavelets, operator spaces and other related areas. This work consists of contributions from invited speakers and some mathematicians who were unable to attend. It presents important mathematical ideas while maintaining the uniqueness and excitement of this very successful event.
Author : William Arveson
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 32,78 MB
Release : 1984
Category : Mathematics
ISBN : 9780821889008
This book contains expanded versions of ten lectures delivered at Texas Tech University in the summer of 1983. The operator algebras of the title are nonselfadjoint algebras of operators on Hilbert space.