$E'$ and its relation with vector-valued functions on $E$.

DANIEL CARANDO; SILVIA LASSALLE

ARKIV FOR MATEMATIK

Springer

Año: 2004 vol. 42 p. 283 - 300

0004-2080

We study the relation between different spaces of vector-valuedpolynomials and analytic functions over dual-isomorphic Banachspaces. Under conditions of regularity on $E$ and $F$, we showthat the spaces of $X$-valued $n$-homogeneous polynomials andanalytic functions of bounded type on $E$ and $F$ are isomorphicwhenever $X$ is a dual space. Also, we prove that many of theusual subspaces of polynomials and analytic functions on $E$ and$F$ are isomorphic without conditions on the involved spaces.