# The Aron–Berner Extension for Polynomials Deﬁned in the Dual of a Banach Space

### José G. Llavona

Universidad Complutense de Madrid, Spain### Luiza A. Moraes

Universidade Federal do Rio de Janeiro, Brazil

## Abstract

Let *E* = *F'* where *F* is a complex Banach space and let π1 : *E''* = *E* ⊕ *F⊥* → *E* be the canonical projection. Let *P*(*nE*) be the space of the complex valued continuous n-homogeneous polynomials deﬁned in *E*. We characterize the elements *P* ∈ *P*(*nE*) whose Aron–Berner extension coincides with *P* ◦ π1 . The case of weakly continuous polynomials is considered. Finally we also study the same problem for holomorphic functions of bounded type.

## Cite this article

José G. Llavona, Luiza A. Moraes, The Aron–Berner Extension for Polynomials Deﬁned in the Dual of a Banach Space. Publ. Res. Inst. Math. Sci. 40 (2004), no. 1, pp. 221–230

DOI 10.2977/PRIMS/1145475970