Extendible Polynomials on Banach Spaces

We are concerned with the following question: when can a polynomial P: EªX Eand X are Banach spaces.be extended to a Banach space containing E? We prove that the polynomials that are extendible to any larger space are precisely those which can be extended to C BEX ., if X is complemented in its bidual, and l B X . in general. We also show that the extendibility is a property that ` E is preserved by Aron]Berner extensions and composition with linear operators. We construct a predual of the space of extendible polynomials for the case that X is a dual space.