Extendible Polynomials on Banach Spaces

Abstract

We are concerned with the following question: when can a polynomialP:E→X(EandXare Banach spaces) be extended to a Banach space containingE? We prove that the polynomials that are extendible to any larger space are precisely those which can be extended toC(BE′), ifXis complemented in its bidual, andl∞(BE′) in general. We also show that the extendibility is a property that is preserved by Aron–Berner extensions and composition with linear operators. We construct a predual of the space of extendible polynomials for the case thatXis a dual space.