Image from Google Jackets

C*-algebras and operator theory / Gerard J. Murphy.

By: Publisher: Boston : Academic Press, �1990Description: 1 online resource (x, 286 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9780080924960
  • 0080924964
  • 1493301640
  • 9781493301645
Subject(s): Genre/Form: Additional physical formats: Print version:: C*-algebras and operator theoryDDC classification:
  • 512/.55 22
LOC classification:
  • QA326 .M87 1990eb
Other classification:
  • *46Lxx
  • 46-02
  • 46H05
  • 46M20
  • 47C15
Online resources:
Contents:
Front Cover ; C*-Algebras and Operator Theory; Copyright Page; Table of Contents; Preface; Chapter 1. Elementary Spectral Theory; 1.1. Banach Algebras; 1.2. The Spectrum and the Spectral Radius; 1.3. The Gelfand Representation; 1.4. Compact and Fredholm Operators; Exercises; Addenda; Chapter 2. C*-Algebras and Hilbert Space Operators; 2.1. C*-Algebras; 2.2. Positive Elements of C*-Algebras; 2.3. Operators and Sesquilinear Forms; 2.4. Compact Hilbert Space Operators; 2.5. The Spectral Theorem; Exercises; Addenda; Chapter 3. Ideals and Positive Functionals; 3.1. Ideals in C*-Algebras.
3.2. Hereditary C*-Subalgebras3.3. Positive Linear Functionals; 3.4. The Gelfand-Naimark Representation; 3.5. Toeplitz Operators; Exercises; Addenda; Chapter 4. Von Neumann Algebras; 4.1. The Double Commutant Theorem; 4.2. The Weak and Ultraweak Topologies; 4.3. The Kaplansky Density Theorem; 4.4. Abelian Von Neumann Algebras; Exercises; Addenda; Chapter 5. Representations of C*-Algebras; 5.1. Irreducible Representations and Pure States; 5.2. The Transitivity Theorem; 5.3. Left Ideals of C*-Algebras; 5.4. Primitive Ideals; 5.5. Extensions and Restrictions of Representations.
5.6. Liminal and Postliminal C*-AlgebrasExercises; Addenda; Chapter 6. Direct Limits and Tensor Products; 6.1. Direct Limits of C*-Algebras; 6.2. Uniformly Hyperfinite Algebras; 6.3. Tensor Products of C*-Algebras; 6.4. Minimality of the Spatial C*-Norm; 6.5. Nuclear C*-Algebras and Short Exact Sequences; Exercises; Addenda; Chapter 7. K-Theory of C*-Algebras; 7.1. Elements of K-Theory; 7.2. The K-Theory of AF-Algebras; 7.3. Three Fundamental Results in K-Theory; 7.4. Stability; 7.5. Bott Periodicity; Exercises; Addenda; Appendix; Notes; References; Notation Index; Subject Index.
Summary: This book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but no prior acquaintance with operator theory is required.
Tags from this library: No tags from this library for this title. Log in to add tags.
Star ratings
    Average rating: 0.0 (0 votes)
Holdings
Item type Current library Call number Status Date due Barcode
E-Books E-Books Central Library, IISER Bhopal Not for loan

Includes bibliographical references (page 279.280) and index.

This book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but no prior acquaintance with operator theory is required.

Print version record.

Front Cover ; C*-Algebras and Operator Theory; Copyright Page; Table of Contents; Preface; Chapter 1. Elementary Spectral Theory; 1.1. Banach Algebras; 1.2. The Spectrum and the Spectral Radius; 1.3. The Gelfand Representation; 1.4. Compact and Fredholm Operators; Exercises; Addenda; Chapter 2. C*-Algebras and Hilbert Space Operators; 2.1. C*-Algebras; 2.2. Positive Elements of C*-Algebras; 2.3. Operators and Sesquilinear Forms; 2.4. Compact Hilbert Space Operators; 2.5. The Spectral Theorem; Exercises; Addenda; Chapter 3. Ideals and Positive Functionals; 3.1. Ideals in C*-Algebras.

3.2. Hereditary C*-Subalgebras3.3. Positive Linear Functionals; 3.4. The Gelfand-Naimark Representation; 3.5. Toeplitz Operators; Exercises; Addenda; Chapter 4. Von Neumann Algebras; 4.1. The Double Commutant Theorem; 4.2. The Weak and Ultraweak Topologies; 4.3. The Kaplansky Density Theorem; 4.4. Abelian Von Neumann Algebras; Exercises; Addenda; Chapter 5. Representations of C*-Algebras; 5.1. Irreducible Representations and Pure States; 5.2. The Transitivity Theorem; 5.3. Left Ideals of C*-Algebras; 5.4. Primitive Ideals; 5.5. Extensions and Restrictions of Representations.

5.6. Liminal and Postliminal C*-AlgebrasExercises; Addenda; Chapter 6. Direct Limits and Tensor Products; 6.1. Direct Limits of C*-Algebras; 6.2. Uniformly Hyperfinite Algebras; 6.3. Tensor Products of C*-Algebras; 6.4. Minimality of the Spatial C*-Norm; 6.5. Nuclear C*-Algebras and Short Exact Sequences; Exercises; Addenda; Chapter 7. K-Theory of C*-Algebras; 7.1. Elements of K-Theory; 7.2. The K-Theory of AF-Algebras; 7.3. Three Fundamental Results in K-Theory; 7.4. Stability; 7.5. Bott Periodicity; Exercises; Addenda; Appendix; Notes; References; Notation Index; Subject Index.

English.

There are no comments on this title.

to post a comment.


Contact for Queries: skpathak@iiserb.ac.in