Questions concerning extensions of polynomials or analytic functions
from a
Banach space E to its bidual E", and others about
reflexivity and related properties on spaces of homogeneous polynomials
Pk(E), have recently spurred interest
regarding the structure of the bidual of a space of polynomials
[4, 14, 22].
In this paper we study the relationship between the bidual of
Pk(E) and the space
of polynomials over E". We define a map through which
elements of the bidual of Pk(E)
may be viewed as polynomials over E"
formula here
and study this map to obtain information about
Pk(E)". We have tried as far
as
possible to avoid imposing restricting conditions on E.