Positive Linear Maps of Operator Algebras
Title | Positive Linear Maps of Operator Algebras PDF eBook |
Author | Erling Størmer |
Publisher | Springer Science & Business Media |
Pages | 135 |
Release | 2012-12-13 |
Genre | Mathematics |
ISBN | 3642343694 |
This volume, setting out the theory of positive maps as it stands today, reflects the rapid growth in this area of mathematics since it was recognized in the 1990s that these applications of C*-algebras are crucial to the study of entanglement in quantum theory. The author, a leading authority on the subject, sets out numerous results previously unpublished in book form. In addition to outlining the properties and structures of positive linear maps of operator algebras into the bounded operators on a Hilbert space, he guides readers through proofs of the Stinespring theorem and its applications to inequalities for positive maps. The text examines the maps’ positivity properties, as well as their associated linear functionals together with their density operators. It features special sections on extremal positive maps and Choi matrices. In sum, this is a vital publication that covers a full spectrum of matters relating to positive linear maps, of which a large proportion is relevant and applicable to today’s quantum information theory. The latter sections of the book present the material in finite dimensions, while the text as a whole appeals to a wider and more general readership by keeping the mathematics as elementary as possible throughout.
Completely Bounded Maps and Operator Algebras
Title | Completely Bounded Maps and Operator Algebras PDF eBook |
Author | Vern Paulsen |
Publisher | Cambridge University Press |
Pages | 316 |
Release | 2002 |
Genre | Mathematics |
ISBN | 9780521816694 |
Table of contents
Introduction to Operator Algebras
Title | Introduction to Operator Algebras PDF eBook |
Author | Bing-Ren Li |
Publisher | World Scientific |
Pages | 758 |
Release | 1992 |
Genre | 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.
Fundamentals of the Theory of Operator Algebras. Volume IV
Title | Fundamentals of the Theory of Operator Algebras. Volume IV PDF eBook |
Author | Richard V. Kadison |
Publisher | American Mathematical Soc. |
Pages | 604 |
Release | 1998-01-13 |
Genre | Mathematics |
ISBN | 0821894684 |
This volume is the companion volume to Fundamentals of the Theory of Operator Algebras. Volume II--Advanced Theory (Graduate Studies in Mathematics series, Volume 16). The goal of the text proper is to teach the subject and lead readers to where the vast literature--in the subject specifically and in its many applications--becomes accessible. The choice of material was made from among the fundamentals of what may be called the "classical" theory of operator algebras. This volume contains the written solutions to the exercises in the Fundamentals of the Theory of Operator Algebras. Volume II--Advanced Theory.
Fundamentals of the Theory of Operator Algebras. V4
Title | Fundamentals of the Theory of Operator Algebras. V4 PDF eBook |
Author | |
Publisher | Academic Press |
Pages | 603 |
Release | 2009-06-01 |
Genre | Mathematics |
ISBN | 0080874193 |
Fundamentals of the Theory of Operator Algebras. V4
Fundamentals of the Theory of Operator Algebras
Title | Fundamentals of the Theory of Operator Algebras PDF eBook |
Author | KADISON |
Publisher | Springer Science & Business Media |
Pages | 599 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461229685 |
These volumes are companions to the treatise; "Fundamentals of the Theory of Operator Algebras," which appeared as Volume 100 - I and II in the series, Pure and Applied Mathematics, published by Academic Press in 1983 and 1986, respectively. As stated in the preface to those volumes, "Their primary goal is to teach the sub ject and lead the reader to the point where the vast recent research literature, both in the subject proper and in its many applications, becomes accessible." No attempt was made to be encyclopcedic; the choice of material was made from among the fundamentals of what may be called the "classical" theory of operator algebras. By way of supplementing the topics selected for presentation in "Fundamentals," a substantial list of exercises comprises the last section of each chapter. An equally important purpose of those exer cises is to develop "hand-on" skills in use ofthe techniques appearing in the text. As a consequence, each exercise was carefully designed to depend only on the material that precedes it, and separated into segments each of which is realistically capable of solution by an at tentive, diligent, well-motivated reader.
Fundamentals of the Theory of Operator Algebras. V2
Title | Fundamentals of the Theory of Operator Algebras. V2 PDF eBook |
Author | |
Publisher | Academic Press |
Pages | 691 |
Release | 1986-06-10 |
Genre | Mathematics |
ISBN | 0080874177 |
Fundamentals of the Theory of Operator Algebras. V2