JournalsprimsVol. 40, No. 1pp. 7–27

Q-reflexive Locally Convex Spaces

  • Christopher Boyd

    University College Dublin, Ireland
  • Seán Dineen

    University College Dublin, Ireland
  • Milena Venkova

    University College Dublin, Ireland
Q-reflexive Locally Convex Spaces cover
Download PDF

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.

Cite this article

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

DOI 10.2977/PRIMS/1145475965