Q-reflexive Locally Convex Spaces
Christopher Boyd
University College Dublin, IrelandSeán Dineen
University College Dublin, IrelandMilena Venkova
University College Dublin, Ireland
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Abstract
For a locally convex space , we use the Aron–Berner extension to define canonical mappings from into different duals of . 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 and . 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