Duality and reflexivity of spaces of approximable polynomials on locally convex spaces
type: Item
instance of: scholarly article
title: Duality and reflexivity of spaces of approximable polynomials on locally convex spaces
zbMATH Open document ID: 0979.46028
author: Christopher Boyd
published in: Monatshefte für Mathematik
publication date: 2002-01-30T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 46G25
Mathematics Subject Classification ID: 46A20
Mathematics Subject Classification ID: 46A11
zbMATH DE Number: 1529490
zbMATH Keywords: \(n\)-homogeneous polynomial
zbMATH Keywords: reflexivity
zbMATH Keywords: Asplund spaces
zbMATH Keywords: biduality
zbMATH Keywords: Fr'echet space
zbMATH Keywords: Radon-Nidodým property
zbMATH Keywords: inductive dual
reviewed by: Rimas Norvaiša
MaRDI profile type: Publication
full work available at URL: s006050070033
OpenAlex ID: W2014591555
DOI: 10.1007/S006050070033
description: scientific article; zbMATH DE number 1529490