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.
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Christopher Boyd, Seán Dineen, Milena Venkova, Q-reﬂexive Locally Convex Spaces. Publ. Res. Inst. Math. Sci. 40 (2004), no. 1, pp. 7–27DOI 10.2977/PRIMS/1145475965