Weakly Compact Composition Operators on Locally Convex Spaces

Let E be a complete, barrelled locally convex space, let V = (v_n) be an increasing sequence of strictly positive, radial, continuous, bounded weights on the unit disc ?? of the complex plane, and let φ be an analytic self map on ??. The composition operators C_φ : f → f ○ φ on the weighted space of holomorphic functions HV (??, E) which map bounded sets into relatively weakly compact subsets are characterized. Our approach requires a study of wedge operators between spaces of continuous linear maps between locally convex spaces which extends results of Saksman and Tylli 31, 32], and a representation of the space HV (??, E) as a space of operators which complements work by Bierstedt , Bonet and Galbis 4] and by Bierstedt and Holtmanns 6].