Kadison and Kastler introduced a natural metric on the collection of all C∗-subalgebras of the bounded operators on a separable Hilbert space. They conjectured that sufficiently close algebras are… (More)

1. Introduction. The investigation leading to this publication was motivated by a desire to try to understand the structure of a linear unital mapping ϕ from a unital algebra A of matrices contained… (More)

Techniques introduced by G. Pisier in his proof that finite von Neumann factors with property Γ have length at most 5 are modified to prove that the length is 3. It is proved that if such a factor is… (More)

The Kadison-Kastler problem asks whether close C*-algebras on a Hilbert space must be spatially isomorphic. We establish this when one of the algebras is separable and nuclear. We also apply our… (More)

This paper addresses a conjecture in the work by Kadison and Kastler [Kadison RV, Kastler D (1972) Am J Math 94:38-54] that a von Neumann algebra M on a Hilbert space H should be unitarily equivalent… (More)

The main result of this paper is that the k continuous Hochschild cohomology groups H(M,M) and H(M, B(H)) of a von Neumann factor M ⊆ B(H) of type II1 with property Γ are zero for all positive… (More)

We construct spectral triples for the Sierpinski gasket as infinite sums of unbounded Fredholm modules associated with the holes in the gasket and investigate their properties. For each element in… (More)

One of the purposes in the computation of cohomology groups is to establish invariants which may be helpful in the classification of the objects under consideration. In the theory of continuous… (More)

On a discrete group G a length function may implement a spectral triple on the reduced group C*-algebra. Following A. Connes, the Dirac operator of the triple then can induce a metric on the state… (More)