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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

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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