Duality and reflexivity of spaces of approximable polynomials on locally convex spaces (Q1585695)

A duality theory for spaces of approximable \(n\)-homogeneous polynomials on locally convex spaces is developed, generalizing results previously obtained for Banach spaces. Let \(E\) be a Fréchet space with its dual having the approximation property and with \(E_b'\) having the local Radon-Nidodým property. The author proved 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 \(E\). When \(E\) is a reflexive Fréchet space, the author also proved that the space of \(n\)-homogeneous polynomials on \(E\) is reflexive if and only if every \(n\)-homogeneous polynomial on \(E\) is boundedly weakly complete.