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ON REFLEXIVITY OF SCALAR-TYPE SPECTRAL OPERATORS

Introduction The aim of the present paper is to give a dual version of the reflexivity result of scalar-type spectral operators in the quasi-complete locally convex spaces proved in [4].The method in our result is based on the barrelled locally convex C(.K*)-modules. Let C(K) be the set of all continuous real or complex valued functions defined on a compact Hausdorff space K with the supremum norm.Suppose that X is a locally convex Hausdorff space. By L*(X) we denote the set of all linear mappings from X into X and by L(X) the set of all continuous linear mappings from X into X. We denote by I the identity operator. The topological dual of X will be denoted by X'. We denote by X" the topological dual of X'[(3{X',X)}. We say that X is a locally convex C(i;i)-module if the bilinear mapping • : C(K) x l > l , (a, x) —» a.x satisfies the following conditions: