Orthogonal scalar products on von Neumann algebras
Orthogonal vector measures on projection lattices in a Hilbert space
Outers for noncommutative revisited
We continue our study of outer elements of the noncommutative spaces associated with Arveson’s subdiagonal algebras. We extend our generalized inner-outer factorization theorem, and our characterization of outer elements, to include the case of elements with zero determinant. In addition, we make several further contributions to the theory of outers. For example, we generalize the classical fact that outers in actually satisfy the stronger condition that there exist aₙ ∈ A with haₙ ∈ Ball(A)...
Pointwise Convergence Theorems in L2 over a von Neumann Algebra.
Positive cones associated with a von Neumann algebra.
Positive operator bimeasures and a noncommutative generalization
For C*-algebras A and B and a Hilbert space H, a class of bilinear maps Φ: A× B → L(H), analogous to completely positive linear maps, is studied. A Stinespring type representation theorem is proved, and in case A and B are commutative, the class is shown to coincide with that of positive bilinear maps. As an application, the extendibility of a positive operator bimeasure to a positive operator measure is shown to be equivalent to various conditions involving positive scalar bimeasures, pairs of...
Positive self-adjoint extensions of operators affiliated with a von Neumann algebra.
Produit croisé d'une algèbre de Kac par un groupe localement compact
Projections from a von Neumann algebra onto a subalgebra
Pure Jauch-Piron states on von Neumann algebras
Quantum dynamical entropy revisited
We define a new quantum dynamical entropy for a C*-algebra automorphism with an invariant state (and for an appropriate 'approximating' subalgebra), which entropy is a 'hybrid' of the two alternative definitions by Connes, Narnhofer and Thirring resp. by Alicki and Fannes (and earlier, Lindblad). We report on this entropy's properties and on three examples.
Quantum logics, vector-valued measures and representations
Quasi *-algebras of measurable operators
Non-commutative -spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For p ≥ 2 they are also proved to possess a sufficient family of bounded positive sesquilinear forms with certain invariance properties. CQ*-algebras of measurable operators over a finite von Neumann algebra are also constructed and it is proven that any abstract CQ*-algebra (,₀) with a sufficient family of bounded positive tracial sesquilinear forms can be represented as a CQ*-algebra...
Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index.
Remarks on joint distributions of observables
Remarks on Nikodým's boundedness theorem.
Représentation de martingales d'opérateurs, d'après Parthasarathy-Sinha
Représentation des fonctions conditionnellement de type positif, d'après V.P. Belavkin
Representations of modules over a *-algebra and related seminorms
Representations of a module over a *-algebra are considered and some related seminorms are constructed and studied, with the aim of finding bounded *-representations of .
Sharp uniform convexity and smoothness inequalities for trace norms.