Real Operator Algebras
Author | : Bingren Li |
Publisher | : World Scientific |
Total Pages | : 264 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 9789812795182 |
Since the treatment is from the beginning (real Banach and Hilbert spaces, real Banach algebras,
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Author | : Bingren Li |
Publisher | : World Scientific |
Total Pages | : 264 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 9789812795182 |
Since the treatment is from the beginning (real Banach and Hilbert spaces, real Banach algebras,
Author | : Kehe Zhu |
Publisher | : CRC Press |
Total Pages | : 172 |
Release | : 1993-05-27 |
Genre | : 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 |
Total Pages | : 424 |
Release | : 2012-12-06 |
Genre | : 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 | : William Arveson |
Publisher | : American Mathematical Soc. |
Total Pages | : 103 |
Release | : 1984 |
Genre | : Mathematics |
ISBN | : 0821807056 |
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.
Author | : Li Bingren |
Publisher | : World Scientific |
Total Pages | : 756 |
Release | : 1992-09-25 |
Genre | : Mathematics |
ISBN | : 9813104511 |
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 | : Bruce Blackadar |
Publisher | : Springer Science & Business Media |
Total Pages | : 530 |
Release | : 2006-03-09 |
Genre | : 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 | : Liming Ge |
Publisher | : American Mathematical Soc. |
Total Pages | : 416 |
Release | : 1998 |
Genre | : 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 | : Maria Amélia Bastos |
Publisher | : Springer Science & Business Media |
Total Pages | : 443 |
Release | : 2008-05-27 |
Genre | : Mathematics |
ISBN | : 3764386843 |
This book is composed of three survey lecture courses and some twenty invited research papers presented to WOAT 2006 - the International Summer School and Workshop on Operator Algebras, Operator Theory and Applications, held at Lisbon in September 2006. The volume reflects recent developments in the area of operator algebras and their interaction with research fields in complex analysis and operator theory. The book is aimed at postgraduates and researchers in these fields.
Author | : A. Katavolos |
Publisher | : Springer Science & Business Media |
Total Pages | : 470 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9401155003 |
During the last few years, the theory of operator algebras, particularly non-self-adjoint operator algebras, has evolved dramatically, experiencing both international growth and interfacing with other important areas. The present volume presents a survey of some of the latest developments in the field in a form that is detailed enough to be accessible to advanced graduate students as well as researchers in the field. Among the topics treated are: operator spaces, Hilbert modules, limit algebras, reflexive algebras and subspaces, relations to basis theory, C* algebraic quantum groups, endomorphisms of operator algebras, conditional expectations and projection maps, and applications, particularly to wavelet theory. The volume also features an historical paper offering a new approach to the Pythagoreans' discovery of irrational numbers.
Author | : M. Takesaki |
Publisher | : Springer Science & Business Media |
Total Pages | : 444 |
Release | : 2001-11-20 |
Genre | : Mathematics |
ISBN | : 9783540422488 |
Since its inception by von Neumann 70 years ago, the theory of operator algebras has become a rapidly developing area of importance for the understanding of many areas of mathematics and theoretical physics. Accessible to the non-specialist, this first part of a three-volume treatise provides a clear, carefully written survey that emphasizes the theory's analytical and topological aspects.