Completely Bounded Maps and Operator Algebras
Published on 2024
In this book, first published in 2003, the reader is provided with a tour of the principal results and ideas in the theories of completely positive maps, completely bounded maps, dilation theory, operator spaces and operator algebras, together with some of their main applications. The author assumes only that the reader has a basic background in functional analysis, and the presentation is self-contained and paced appropriately for graduate students new to the subject. Experts will also want this book for their library since the author illustrates the power of methods he has developed with new and simpler proofs of some of the major results in the area, many of which have not appeared earlier in the literature. An indispensable introduction to the theory of operator spaces for all who want to know more.
Completely Bounded Maps and Operator Algebras
In this book, first published in 2003, the reader is provided with a tour of the principal results and ideas in the theories of completely positive maps, completely bounded maps, dilation theory, operator spaces and operator algebras, together with some of their main applications. The author assumes only that the reader has a basic background in functional analysis, and the presentation is self-contained and paced appropriately for graduate students new to the subject. Experts will also want this book for their library since the author illustrates the power of methods he has developed with new and simpler proofs of some of the major results in the area, many of which have not appeared earlier in the literature. An indispensable introduction to the theory of operator spaces for all who want to know more.
Lectures on von Neumann Algebras
Published on 2019
Written in lucid language, this valuable text discusses fundamental concepts of von Neumann algebras including bounded linear operators in Hilbert spaces, finite von Neumann algebras, linear forms on algebra of operators, geometry of projections and classification of von Neumann algebras in an easy to understand manner. The revised text covers new material including the first two examples of factors of type II^1, an example of factor of type III and theorems for von Neumann algebras with a cyclic and separating vector. Pedagogical features including solved problems and exercises are interspersed throughout the book.
- New topics including the first two examples of factors of type II^1, an example of factor of type III and theorems for von Neumann algebras are discussed in detail
- Covers the theory of standard von Neumann algebras, first in the classical semi-finite case, then in the case where there is a cyclic and separating vector, and finally in general cases
- Pedagogical features including solved problems and exercises are interspersed throughout the book
Lectures on von Neumann Algebras
Written in lucid language, this valuable text discusses fundamental concepts of von Neumann algebras including bounded linear operators in Hilbert spaces, finite von Neumann algebras, linear forms on algebra of operators, geometry of projections and classification of von Neumann algebras in an easy to understand manner. The revised text covers new material including the first two examples of factors of type II^1, an example of factor of type III and theorems for von Neumann algebras with a cyclic and separating vector. Pedagogical features including solved problems and exercises are interspersed throughout the book.
- New topics including the first two examples of factors of type II^1, an example of factor of type III and theorems for von Neumann algebras are discussed in detail
- Covers the theory of standard von Neumann algebras, first in the classical semi-finite case, then in the case where there is a cyclic and separating vector, and finally in general cases
- Pedagogical features including solved problems and exercises are interspersed throughout the book