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Abelian subalgebras of von Neumann algebras
About this Title
Donald Bures
Publication: Memoirs of the American Mathematical Society
Publication Year:
1971; Number 110
ISBNs: 978-0-8218-1810-7 (print); 978-0-8218-9907-6 (online)
DOI: https://doi.org/10.1090/memo/0110
MathSciNet review: 0296706
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