We characterize the compact multiplication operators on a semicrossed product $C_0(X)\times _\phi \mathbb Z_+$ in terms of corresponding dynamical system. also elements this algebra and determine ideal they generate.

Let X be a completely regular Hausdorff space, let V be a system of weights on X and let T be a locally convex Hausdorff topological vector space. Then CVb(X, T) is a locally convex space of vector-valued continuous functions with a topology generated by seminorms which are weighted analogues of the supremum norm. In the present paper we characterize multiplication operators on the space CVb(X,...

A linear operator on a Hilbert space may be approximated with nite matrices by choosing an orthonormal basis of the Hilbert space. For an operator that is not compact such approximations cannot converge in the norm topology on the space of operators. Multiplication operators on spaces of L2 functions are never compact; for them we consider how well the eigenvalues of the matrices approximate th...