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Decompositions of Operator Algebras, I and II
eBook ISBN:  9781470400392 
Product Code:  MEMO/1/9.E 
List Price:  $20.00 
MAA Member Price:  $18.00 
AMS Member Price:  $12.00 
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Decompositions of Operator Algebras, I and II
eBook ISBN:  9781470400392 
Product Code:  MEMO/1/9.E 
List Price:  $20.00 
MAA Member Price:  $18.00 
AMS Member Price:  $12.00 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 1; 1951; 133 ppMSC: Primary 16

Table of Contents

Chapters

Volume I

1. Introduction

2. Definitions and notations

3. Decomposition of a state relative to a commutative algebra

4. Direct integrals of Hilbert spaces

5. Maximal decompositions

Part I. Applications

6. Decomposition of a $W^*$algebra into factors

7. Decomposition of a group representation into irreducible representations

8. Decomposition of an invariant measure into ergodic parts

9. The Fourier transform for separable unimodular groups

10. Deflation of decompositions

Volume II. Multiplicity theory

1. Introduction

Part I. Commutative algebras

2. Definitions and technical preliminaries

3. Structure of maximal abelian $W^*$algebras

4. Structure of commutative $W^*$algebras

5. Unitary invariants of commutative $W^*$algebras and of $SA$ operators

6. Applications

Part II. Noncommutative algebras

7. Decomposition theory

8. Algebras of uniform multiplicity

9. Algebras of type I


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Chapters

Volume I

1. Introduction

2. Definitions and notations

3. Decomposition of a state relative to a commutative algebra

4. Direct integrals of Hilbert spaces

5. Maximal decompositions

Part I. Applications

6. Decomposition of a $W^*$algebra into factors

7. Decomposition of a group representation into irreducible representations

8. Decomposition of an invariant measure into ergodic parts

9. The Fourier transform for separable unimodular groups

10. Deflation of decompositions

Volume II. Multiplicity theory

1. Introduction

Part I. Commutative algebras

2. Definitions and technical preliminaries

3. Structure of maximal abelian $W^*$algebras

4. Structure of commutative $W^*$algebras

5. Unitary invariants of commutative $W^*$algebras and of $SA$ operators

6. Applications

Part II. Noncommutative algebras

7. Decomposition theory

8. Algebras of uniform multiplicity

9. Algebras of type I
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