Duality and Reflexivity of Spaces of Approximable Polynomials on Locally Convex Spaces |
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Authors: | Christopher Boyd |
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Affiliation: | (1) University College Dublin, Ireland, IE |
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Abstract: | We develop a duality theory for spaces of approximable n-homogeneous polynomials on locally convex spaces, generalising results previously obtained for Banach spaces. For E a Fréchet space with its dual having the approximation property and with E′ b locally Asplund we show that the space of n-homogeneous polynomials on (E′ b )′ b is the inductive dual of the space of boundedly weakly continuous n-homogeneous polynomials on E. We show that when E is a reflexive Fréchet space, the space of n-homogeneous polynomials on E is reflexive if and only if every n-homogeneous polynomial on E is boundedly weakly continuous. (Received 24 March 1999; in final form 14 February 2000) |
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Keywords: | 1991 Mathematics Subject Classification: 46G20 46G20 46A20 46A11 |
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