Inequalities in Von Neumann Algebras
Inner ideals in C*-algebras.
Inner one-parameter groups acting on a factor.
Integrable group actions on von Neumann algebras.
Invariant states and a conditional fixed point property for affine actions.
Invariant states for positive operator semigroups
Invariant States of von Neumann Algebras.
Invariant Weights on Semi-Finite von Neumann Algebras.
Isomorphisms of Large Ideals of AW*-Algebras.
Kernel Operators on Lp-spaces Associated with Semifinite von Neumann Algebras.
Krein-space operators determined by free product algebras induced by primes and graphs
In this paper, we introduce certain Krein-space operators induced by free product algebras induced by both primes and directed graphs. We study operator-theoretic properties of such operators by computing free-probabilistic data containing number-theoretic data.
L2 Riemannian-Roch Theorem for Elliptic Operators.
L²-homology and reciprocity for right-angled Coxeter groups
Let W be a Coxeter group and let μ be an inner product on the group algebra ℝW. We say that μ is admissible if it satisfies the axioms for a Hilbert algebra structure. Any such inner product gives rise to a von Neumann algebra containing ℝW. Using these algebras and the corresponding von Neumann dimensions we define -Betti numbers and an -Euler charactersitic for W. We show that if the Davis complex for W is a generalized homology manifold, then these Betti numbers satisfy a version of Poincaré...
Les algèbres hilbertiennes modulaires de Tomita
Les facteurs de von Neumann de type III
Long-Time Asymptotic Properties of Dynamical Semigroups on W*-algebras.
Majorizations for Generalized s-Numbers in Semifinite von Neumann Algebras.
Markovian processes on mutually commuting von Neumann algebras
The aim of this paper is to study markovianity for states on von Neumann algebras generated by the union of (not necessarily commutative) von Neumann subagebras which commute with each other. This study has been already begun in [2] using several a priori different notions of noncommutative markovianity. In this paper we assume to deal with the particular case of states which define odd stochastic couplings (as developed in [3]) for all couples of von Neumann algebras involved. In this situation...
Martingales in Banach *-algebras.
Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs
In this paper, we study groupoid actions acting on arithmetic functions. In particular, we are interested in the cases where groupoids are generated by directed graphs. By defining an injective map α from the graph groupoid G of a directed graph G to the algebra A of all arithmetic functions, we establish a corresponding subalgebra AG = C*[α(G)]︀ of A. We construct a suitable representation of AG, determined both by G and by an arbitrarily fixed prime p. And then based on this representation, we...