The Aron–Berner Extension for Polynomials Deﬁned in the Dual of a Banach Space
José G. LlavonaUniversidad Complutense de Madrid, Spain
Luiza A. MoraesUniversidade Federal do Rio de Janeiro, Brazil
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. 221–230DOI 10.2977/PRIMS/1145475970