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Abelian Subalgebras of Von Neumann Algebras
Available Formats:
Electronic ISBN: 9780821899076
Product Code: MEMO/1/110.E
List Price: $20.00
MAA Member Price: $18.00
AMS Member Price: $12.00
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Abelian Subalgebras of Von Neumann Algebras
Available Formats:
Electronic ISBN:  9780821899076 
Product Code:  MEMO/1/110.E 
List Price:  $20.00 
MAA Member Price:  $18.00 
AMS Member Price:  $12.00 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 1; 1971; 127 ppMSC: Primary 46; Secondary 28; 47;

Table of Contents

Chapters

Introduction

Remarks on notation

Part I. Multiplicity in factors of type $\textrm {II}_1$

1. The multiplicity of a projection

2. The normal case

3. The general case

Part II. The von Neumann construction of factors

4. $\mathcal {M}$groups with $\mathcal {M}$ abelian

5. $\mathcal {M}$groups

6. Subalgebras $\mathcal {M}$ of $\mathcal {A}$ with $\mathcal {A}$ strongly finite over $\mathcal {M}$

7. Substantial subalgebras

8. Relations between the type of $\mathcal {A}$ and the type of $G(\mathcal {A,M})$

9. Construction of $\mathcal {A}$ containing a substantial subalgebra $\mathcal {M}$ with $G(\mathcal {A,M})$ a given full $\mathcal {M}$group

Part III. Thick subalgebras

10. Elementary properties

11. Strong orthogonality

12. A method for constructing thick subalgebras

13. Methods for determining the deficiency type and the multiplicity function

14. Dixmier’s example

15. Some examples of thick subalgebras


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 Book Details
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Volume: 1; 1971; 127 pp
MSC: Primary 46; Secondary 28; 47;

Chapters

Introduction

Remarks on notation

Part I. Multiplicity in factors of type $\textrm {II}_1$

1. The multiplicity of a projection

2. The normal case

3. The general case

Part II. The von Neumann construction of factors

4. $\mathcal {M}$groups with $\mathcal {M}$ abelian

5. $\mathcal {M}$groups

6. Subalgebras $\mathcal {M}$ of $\mathcal {A}$ with $\mathcal {A}$ strongly finite over $\mathcal {M}$

7. Substantial subalgebras

8. Relations between the type of $\mathcal {A}$ and the type of $G(\mathcal {A,M})$

9. Construction of $\mathcal {A}$ containing a substantial subalgebra $\mathcal {M}$ with $G(\mathcal {A,M})$ a given full $\mathcal {M}$group

Part III. Thick subalgebras

10. Elementary properties

11. Strong orthogonality

12. A method for constructing thick subalgebras

13. Methods for determining the deficiency type and the multiplicity function

14. Dixmier’s example

15. Some examples of thick subalgebras
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