MULTIPLICATION OPERATORS AND DYNAMICAL-SYSTEMS ON WEIGHTED SPACES OF CROSS-SECTIONS

Let Y be a Hausdorff topological space, let V be a system of weights o n Y, and let LV0(Y) and LV(b)(Y) be the weighted locally convex spaces of cross-sections with a topology generated by seminorms which are we ighted analogues of the supremum norm. In the present paper, we charac terise the multiplication operators on the spaces LV0(Y) and LV(b)(Y) induced by the scalar-valued, the vector-valued, and the operator-valu ed mappings. A (linear) dynamical system on the weighted spaces of cro ss-sections is obtained as an application of the theory of the multipl ication operators. Many examples are given to illustrate the theory.