Q-reflexive Locally Convex Spaces

Abstract

For a locally convex space E we use the Aron–Berner extension to define canonical mappings from ⊗^s,n,π\_E''e\_ into different duals of P(n\_\_E). We investigate necessary and suffcient conditions for the continuity of these mappings, paying particular attention to three special cases — Fréchet spaces, DF spaces and reflexive A-nuclear spaces. We define Q-reflexive spaces as spaces where a certain canonical mapping can be extended to an isomorphism between ⊗^s,n,π\_E''e\_ and (P(n\_\_E), τ\_b\_)'i. We find examples of such spaces.