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Abelian Subalgebras of Von Neumann Algebras

Available Formats:
Electronic ISBN: 978-0-8218-9907-6
Product Code: MEMO/1/110.E
List Price: $20.00 MAA Member Price:$18.00
AMS Member Price: $12.00 Click above image for expanded view Abelian Subalgebras of Von Neumann Algebras Available Formats:  Electronic ISBN: 978-0-8218-9907-6 Product Code: MEMO/1/110.E  List Price:$20.00 MAA Member Price: $18.00 AMS Member Price:$12.00
• Book Details

Memoirs of the American Mathematical Society
Volume: 11971; 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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 11971; 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
Review Copy – for reviewers who would like to review an AMS book
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