Let [Formula: see text] be a compact metric space and let continuous. We study text]-algebra generated by all multiplication operators continuous functions on composition operator induced certain space. system of proper contractions text]. Suppose that are inverse branches is self-similar. consider the Hutchinson measure Then we show C[Formula: isomorphic to associated with under some conditions.

We characterize the common range of adjoints cyclic multiplication operators on Drury-Arveson space. show that a function belongs to this if and only its Taylor coefficients satisfy simple decay condition. To achieve this, we introduce uniform Smirnov class ball determine dual space equals strictly smaller space, in turn operators.

Let A be a Banach algebra. For f ∈ A*, we inspect the weak sequential properties of well-known map Tf : → (a) = fa, where fa A* is defined by fa(x) (ax) for all x A. We provide equivalent conditions when completely continuous every and maps weakly precompact sets onto L-sets A*. Our results have applications to algebra compact operators K(X) on space X.

In this paper we study the properties of multiplication invariant (MI) operators acting on subspaces vector-valued space L2(X;H). We characterize such in terms range functions by showing that there is an isomorphism between category MI spaces (with as morphisms) and measurable whose morphisms are operators. investigate how global operator reflected local pointwise its corresponding operator. al...