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Crossed products of von Neumann algebras by equivalence relations and their subalgebras
About this Title
Igor Fulman
Publication: Memoirs of the American Mathematical Society
Publication Year:
1997; Volume 126, Number 602
ISBNs: 978-0-8218-0557-2 (print); 978-1-4704-0187-0 (online)
DOI: https://doi.org/10.1090/memo/0602
MathSciNet review: 1371091
MSC: Primary 46L45; Secondary 46L10, 46L55, 47D25
Table of Contents
Chapters
- 1. Introduction
- 2. Preliminaries
- 3. Unitary realization of $\alpha _{(y,x)}$
- 4. Construction of $\tilde {M}^\nabla$
- 5. Coordinate representation of elements of $M$
- 6. The expectation $E$
- 7. Coordinates in $\tilde {M}^\nabla$
- 8. The expectation $E’$
- 9. Tomita-Takesaki theory for $\tilde {M}$ and $\tilde {M}^\nabla$
- 10. $I(M)$-automorphisms of $\tilde {M}$
- 11. Flows of automorphisms
- 12. The Feldman-Moore-type structure theorem
- 13. Isomorphisms of crossed products
- 14. Bimodules and subalgebras of $\tilde {M}$
- 15. Spectral theorem for bimodules
- 16. Analytic algebra of a flow of automorphisms
- 17. Properties of $\tilde {M}$
- 18. Hyperfiniteness and dilations
- 19. The construction of Yamanouchi
- 20. Examples and particular cases