No abstract

No abstract

A unital C*-algebra is said to satisfy the Dixmier property if for each element x in the closed convex hull of all elements of the form u*xu, u being a unitary in , intersects the centre of ((2), 2·7). The von Neumann algebras and also some other classes of C*-algebras are known to satisfy the Dixmier property (cf. (2), (3), (4), (6)). If is a simple C*-algebra which satisfies the Dixmier property then has at most one tracial state. In (3) Archbold raised the question whether there exists a unital simple C*-algebra which has at most one tracial state without satisfying the Dixmier property. In the present note we characterize the unital simple C*-algebras with at most one tracial state in terms of a condition which is similar to the Dixmier property, but is in fact formally weaker in the framework of simple C*-algebras. This characterization relies on the method used by Pedersen in (5) in order to show that for a unital simple C*-algebra which has at most one tracial state and at least one non-trivial projection the linear span of all projections in is dense in As an application we characterize those unital simple C*-algebras with a unique tracial state which satisfy the Dixmier property.

Abstract. We give a series of examples of simple finitely generated dimension groups which cannot be obtained as the inductive limit of a systemwhere each A" is a unimodular matrix whose entries are nonnegative integers.

It is shown that any von Neumann algebra 9H with a cyclic and separating vector can be decomposed into factors in such a manner that the type of 9IL is preserved under this decomposition. In the present paper we shall use the theory of standard von Neumann algebras, as well as Choquet theory, in order to show that any von Neumann algebra tyίl with a cyclic and separating vector can be decomposed into factors in such a manner that the factors which occur in the decomposition preserve the type of 911. For a semifinite von Neumann algebra we shall prove a stronger result, namely there exists a disintegration of the traces which are defined on the positive cone Introduction