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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

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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