engleski

Elementary operators and subhomogeneous C*-algebras

Let A be a C*-algebra and let $\Theta_A$ be the canonical contraction form the Haagerup tensor product of M(A) with itself to the space of completely bounded maps on A. In this paper we consider the following conditions on A: (a) A is a finitely generated module over the centre of M(A) ; (b) the image of ΘA is equal to the set E(A) of all elementary operators on A ; and (c) the lengths of elementary operators on A are uniformly bounded. We show that A satisfies (a) if and only if it is a finite direct sum of unital homogeneous C*-algebras. We also show that if a separable A satisfies (b) or (c), then A is necessarily subhomogeneous and the C*-bundles corresponding to the homogeneous subquotients of A must be of finite type.

C*-algebra ; subhomogeneous ; elementary operators

nije evidentirano