Completely bounded maps and operator algebras / Vern Paulsen.

Format:

Book

Author/Creator:

Paulsen, Vern I., 1951- author.

Series:

Cambridge studies in advanced mathematics ; 78.

Cambridge studies in advanced mathematics ; 78

Language:

English

Subjects (All):

Operator algebras.

Dilation theory (Operator theory).

Mappings (Mathematics).

Physical Description:

1 online resource (xii, 300 pages) : digital, PDF file(s).

Edition:

1st ed.

Other Title:

Completely Bounded Maps & Operator Algebras

Place of Publication:

Cambridge : Cambridge University Press, 2002.

Language Note:

English

Summary:

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.

Contents:

1. Introduction

2. Positive Maps

3. Completely Positive Maps

4. Dilation Theorems

5. Commuting Contractions on Hilbert Space

6. Completely Positive Maps into M[subscript n]

7. Arveson's Extension Theorems

8. Completely Bounded Maps

9. Completely Bounded Homomorphisms

10. Polynomially Bounded and Power-Bounded Operators

11. Applications to K-Spectral Sets

12. Tensor Products and Joint Spectral Sets

13. Abstract Characterizations of Operator Systems and Operator Spaces

14. An Operator Space Bestiary

15. Injective Envelopes

16. Abstract Operator Algebras

17. Completely Bounded Multilinear Maps and the Haagerup Tensor Norm

18. Universal Operator Algebras and Factorization

19. Similarity and Factorization.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 285-295) and index.

ISBN:

1-107-13453-6

1-280-42008-1

9786610420087

1-139-14839-7

0-511-16960-4

0-511-05470-X

0-511-30273-8

0-511-54663-7

0-511-06949-9

OCLC:

228110971