Semigroups of Operators on Locally Convex Spaces

On a Theorem of Zabczyk for Semigroups of Operators in Locally Convex Spaces

The purpose of this paper is to extend a stability theorem of Zabczyk to the case of semigroups of operators in locally convex topological vector spaces. Obtained results generalize the similar theorems proved by Datko, Pazy, Rolewicz and Littman for the case of C0-semigroups of operators in Banach spaces. AMS Mathematics Subject Classification (2000): 34D05,34D20

Banach Algebras of Operators on Locally Convex Spaces

On the dual of certain locally convex function spaces

In this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $X$,  where $X$ is a $C$-distinguished topological space. Then, we show that their dual spaces can be identified in a natural way with certain spaces of Radon measures.

Hyperinvariant Subspaces for Some Operators on Locally Convex Spaces

Some results concerning hyperinvariant subspaces of some operators on locally convex spaces are considered. Denseness of a class of operators which have a hyperinvariant subspace in the algebra of locally bounded operators is proved.

On reducibility of some operator semigroups and algebras on locally convex spaces

Let X be a complex Hausdorff locally convex space. A system of seminorms P inducing the topology on X will be called a calibration. We denote by (X) the collection of all calibrations on X . For a given P ∈ (X) let P = {pα : α ∈ ∆}, where ∆ is some index set and for each α ∈ ∆ denote Uα = {x : pα(x) ≤ 1}. Let us denote by (X) the set of all linear continuous operators on X , by (X) the set of c...