Journal ArticleDOI
Coordinates for triangular operator algebras
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In this article, theoreme de structure for des algebres sous diagonales contenant une sous algebre de Cartan was demontre.Abstract:
On demontre un theoreme de structure pour des algebres sous diagonales contenant une sous algebre de Cartan. On etudie les isomorphismes pour ces algebresread more
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Structure for regular inclusions. i
TL;DR: In this paper, the authors studied pairs (C,D) of unital C*-algebras where D is a regular abelian C*subalgebra of C and showed that the left kernel of E, L(C, D), is the unique closed two-sided ideal of C maximal with respect to having trivial intersection with D.
Journal ArticleDOI
Amenable equivalence relations and turing degrees
TL;DR: In [12] Slaman and Steel posed the following problem: Assume ZF + DC + AD must the rationals embed order preservingly in <_d for a cone of d's?
Journal ArticleDOI
Triangular algebras and ideals of nest algebras
TL;DR: The maximal triangular algebras of operators have been studied for 30 years now, since the seminal paper of Kadison and Singer [6] as mentioned in this paper, who proposed the maximal triangular algebra as infinitedimensional generalizations of the upper triangular matrices and as the non-self-adjoint analogues of the von Neumann alges.
Book ChapterDOI
The Structure of Borel Equivalence Relations in Polish Spaces
TL;DR: In this article, a general Glimm-Effros dichotomy for Borel equivalence relations and a study of countable Borel relations and their classification into subclasses such as smooth, hyperfinite, amenable, treeable etc.
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Journal ArticleDOI
Ergodic equivalence relations, cohomology, and von Neumann algebras. II
J. Feldman,Calvin C. Moore +1 more
Classification of injective factors
TL;DR: Nann et al. as mentioned in this paper presented a survey of the main lines of the investigation in the classification of factors, culminating in the Connes-Takesakl structure theory of type III factors.
Journal ArticleDOI
Une classification des facteurs de type ${\rm III}$
Journal ArticleDOI
Ergodic equivalence relations, cohomology, and von Neumann algebras
J. Feldman,Calvin C. Moore +1 more
Journal ArticleDOI
Conditional Expectations in von Neumann Algebras
TL;DR: In this article, it was shown that a von Neumann algebra M is invariant under modular automorphism group σtϑ associated with ϑ if and only if there exists a σ-weakly continuous faithful projection ϵ of norm one from M onto N such that ϑ(x) = ϑ ∘ ϵ(x), for every xϵMϑ.