Fundamentals of the Theory of Operator Algebras. V2

Fundamentals of the Theory of Operator Algebras. V2

Advanced Theory

1st Edition - June 10, 1986

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  • Editors: Richard V. Kadison, John R. Ringrose
  • eBook ISBN: 9780080874173

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Table of Contents

  • Preface

    Contents of Volume I

    Chapter 1 Linear Spaces

    Chapter 2 Basics of Hilbert Space and Linear Operators

    Chapter 3 Banach Algebras

    Chapter 4 Elementary C*-Algebra Theory

    Chapter 5 Elementary von Neumann Algebra Theory

    Chapter 6: Comparison Theory of Projections

    6.1 Polar decomposition and equivalence

    6.2 Ordering

    6.3 Finite and infinite projections

    6.4 Abelian projections

    6.5 Type decomposition

    6.6 Type I algebras

    6.7 Example

    6.7.1 Lemma

    6.7.2 Theorem

    6.7.3 Remark

    6.7.4 Proposition

    6.7.5 Theorem

    6.7.6 Example

    6.7.7 Example

    6.7.8 Theorem

    6.7.9 Remark

    6.7.10 Theorem

    6.8 Ideals

    6.9 Exercises

    Chapter 7: Normal States and Unitary Equivalence of Von Neumann Algebras

    7.1 Completely additive states

    7.2 Vector states and unitary implementation

    7.3 A second approach to normal states

    7.4 The predual

    7.5 Normal weights on von Neumann algebras

    7.6 Exercises

    Chapter 8: The Trace

    8.1 Traces

    8.2 The trace in finite algebras

    8.3 The Dixmier approximation Theorem

    8.4 The dimension function

    8.5 Tracial weights on factors

    8.6 Further examples of factors

    8.7 Exercises

    Chapter 9: Algebra and Commutant

    9.1 The type of the commutant

    9.2 Modular theory

    9.3 Unitary equivalence of type I algebras

    9.4 Abelian von Neumann algebras

    9.5 Spectral multiplicity

    9.6 Exercises

    Chapter 10: Special Representations of C*-Algebras

    10.1 The universal representation

    10.2 Irreducible representations

    10.3 Disjoint representations

    10.4 Examples

    10.5 Exercises

    Chapter 11: Tensor Products

    11.1 Tensor products of represented C*-algebras

    11.2 Tensor products of von Neumann algebras

    11.3 Tensor products of abstract C*-algebras

    11.4 Infinite tensor products of C*-algebras

    11.5 Exercises

    Chapter 12: Approximation by Matrix Algebras

    12.1 Isomorphism of uniformly matricial algebras

    12.2 The finite matricial factor

    12.3 States and representations of matricial C*-algebras

    12.4 Exercises

    Chapter 13: Crossed Products

    13.1 Discrete crossed products

    13.2 Continuous crossed products

    13.3 Crossed products by modular automorphism groups

    13.4 Exercises

    Chapter 14: Direct Integrals and Decompositions

    14.1 Direct integrals

    14.2 Decompositions relative to abelian algebras

    14.3 Appendix—Borel mappings and analytic sets

    14.4 Exercises


    Index of Notation

    Algebras and related matters

    Direct sums and integrals

    Equivalences and orderings

    Inner products and norms

    Linear operators

    Linear spaces

    Linear topological spaces, Banach spaces, Hilbert spaces

    Modular theory

    Multiplicity theory

    Sets and mappings

    Special Banach spaces

    States and weights

    Tensor products and crossed products


Product details

  • No. of pages: 675
  • Language: English
  • Copyright: © Academic Press 1986
  • Published: June 10, 1986
  • Imprint: Academic Press
  • eBook ISBN: 9780080874173

About the Serial Editors

Richard V. Kadison

Affiliations and Expertise

Department of Mathematics, University of Pennsylvania,Philadelphia, Pennsylvania

John R. Ringrose

Affiliations and Expertise

School of Marhematics, University of Newcastle, Newcastle upon Tyne, England

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