Operator Algebras and Their Modules - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Operator Algebras and Their Modules write by David P. Blecher. This book was released on 2004. Operator Algebras and Their Modules available in PDF, EPUB and Kindle. This invaluable reference is the first to present the general theory of algebras of operators on a Hilbert space, and the modules over such algebras. The new theory of operator spaces is presented early on and the text assembles the basic concepts, theory and methodologies needed to equip a beginning researcher in this area. A major trend in modern mathematics, inspired largely by physics, is toward noncommutative' or quantized' phenomena. In functional analysis, this has appeared notably under the name of operator spaces', which is a variant of Banach spaces which is particularly appropriate for solving problems concerning spaces or algebras of operators on Hilbert space arising in 'noncommutative mathematics'. The category of operator spaces includes operator algebras, selfadjoint (that is, C*-algebras) or otherwise. Also, most of the important modules over operator algebras are operator spaces. A common treatment of the subjects of C*-algebras, Non-selfadjoint operator algebras, and modules over such algebras (such as Hilbert C*-modules), together under the umbrella of operator space theory, is the main topic of the book. A general theory of operator algebras, and their modules, naturally develops out of the operator space methodology. Indeed, operator space theory is a sensitive enough medium to reflect accurately many important non-commutative phenomena. Using recent advances in the field, the book shows how the underlying operator space structure captures, very precisely, the profound relations between the algebraic and the functional analytic structures involved. The rich interplay between spectral theory, operator theory, C*-algebra and von Neumann algebra techniques, and the influx of important ideas from related disciplines, such as pure algebra, Banach space theory, Banach algebras, and abstract function theory is highlighted. Each chapter ends with a lengthy section of notes containing a wealth of additional information.
Introduction to Vertex Operator Algebras and Their Representations
Introduction to Vertex Operator Algebras and Their Representations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Vertex Operator Algebras and Their Representations write by James Lepowsky. This book was released on 2012-12-06. Introduction to Vertex Operator Algebras and Their Representations available in PDF, EPUB and Kindle. * Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples. * Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications. * Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics.
Operator Algebras and Applications
Operator Algebras and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Operator Algebras and Applications write by A. Katavolos. This book was released on 2012-12-06. Operator Algebras and Applications available in PDF, EPUB and Kindle. 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.
Hilbert C*-Modules
Hilbert C*-Modules - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Hilbert C*-Modules write by E. Christopher Lance. This book was released on 1995-03-16. Hilbert C*-Modules available in PDF, EPUB and Kindle. Hilbert C*-modules are objects like Hilbert spaces, except that the inner product, instead of being complex valued, takes its values in a C*-algebra. The theory of these modules, together with their bounded and unbounded operators, is not only rich and attractive in its own right but forms an infrastructure for some of the most important research topics in operator algebras. This book is based on a series of lectures given by Professor Lance at a summer school at the University of Trondheim. It provides, for the first time, a clear and unified exposition of the main techniques and results in this area, including a substantial amount of new and unpublished material. It will be welcomed as an excellent resource for all graduate students and researchers working in operator algebras.
On Axiomatic Approaches to Vertex Operator Algebras and Modules
On Axiomatic Approaches to Vertex Operator Algebras and Modules - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On Axiomatic Approaches to Vertex Operator Algebras and Modules write by Igor Frenkel. This book was released on 1993. On Axiomatic Approaches to Vertex Operator Algebras and Modules available in PDF, EPUB and Kindle. The basic definitions and properties of vertex operator algebras, modules, intertwining operators and related concepts are presented, following a fundamental analogy with Lie algebra theory. The first steps in the development of the general theory are taken, and various natural and useful reformulations of the axioms are given. In particular, tensor products of algebras and modules, adjoint vertex operators and contragradient modules, adjoint intertwining operators and fusion rules are studied in greater depth. This paper lays the monodromy-free axiomatic foundation of the general theory of vertex operator algebras, modules and intertwining operators.
