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.
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(Received 24 March 1999; in final form 14 February 2000)
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Boyd, C. Duality and Reflexivity of Spaces of Approximable Polynomials on Locally Convex Spaces. Mh Math 130, 177–188 (2000). https://doi.org/10.1007/s006050070033
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DOI: https://doi.org/10.1007/s006050070033