Positive cones associated with a von Neumann algebra.
Positive self-adjoint extensions of operators affiliated with a von Neumann algebra.
Preliminary algebras arising from local homeomorphisms.
Projections from a von Neumann algebra onto a subalgebra
Property T for discrete groups in terms of their regular representation.
Pseudotopologies with applications to one-parameter groups, von Neumann algebras, and Lie algebra representations
For any pair E,F of pseudotopological vector spaces, we endow the space L(E,F) of all continuous linear operators from E into F with a pseudotopology such that, if G is a pseudotopological space, then the mapping L(E,F) × L(F,G) ∋ (f,g) → gf ∈ L(E,G) is continuous. We use this pseudotopology to establish a result about differentiability of certain operator-valued functions related with strongly continuous one-parameter semigroups in Banach spaces, to characterize von Neumann algebras, and to establish...
Pure Jauch-Piron states on von Neumann algebras
Quasianalytic vectors and derivations of operator algebras.
Quelques résultats dans la théorie algébrique de la diffusion
Radial functions on free groups and a decomposition of the regular representation into irreducible components.
Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index.
Relative commutant algebras of Powers' binary shifts on the hyperfinite II... factor.
Relative Commutant of a von Neumann Algebra in Its Crossed Product by a Group Action.
Relative property (T) and linear groups
Relative property (T) has recently been used to show the existence of a variety of new rigidity phenomena, for example in von Neumann algebras and the study of orbit-equivalence relations. However, until recently there were few examples of group pairs with relative property (T) available through the literature. This motivated the following result: A finitely generated group admits a special linear representation with non-amenable -Zariski closure if and only if it acts on an Abelian group (of...
Remarks on the complementability of spaces of Bochner integrable functions in spaces of vector measures
In the paper [5] L. Drewnowski and the author proved that if is a Banach space containing a copy of then is not complemented in and conjectured that the same result is true if is any Banach space without the Radon-Nikodym property. Recently, F. Freniche and L. Rodriguez-Piazza ([7]) disproved this conjecture, by showing that if is a finite measure and is a Banach lattice not containing copies of , then is complemented in . Here, we show that the complementability of in together...
Rigidity results for Bernoulli actions and their von Neumann algebras
Using very original methods from operator algebras, Sorin Popa has shown that the orbit structure of the Bernoulli action of a property (T) group, completely remembers the group and the action. This information is even essentially contained in the crossed product von Neumann algebra. This is the first von Neumann strong rigidity theorem in the literature. The same methods allow Popa to obtain II factors with prescribed countable fundamental group.
Selfadjoint Extension Operators Commuting with an Algebra.
Semiregular maximal abelian *-subalgebras and the solution to the factor state Stone-Weierstrass problem.
Semisimplicity and global dimension of a finite von Neumann algebra
We prove that a finite von Neumann algebra is semisimple if the algebra of affiliated operators of is semisimple. When is not semisimple, we give the upper and lower bounds for the global dimensions of and This last result requires the use of the Continuum Hypothesis.
Simplicity of the projective unitary groups defined by simple factors.