JournalsprimsVol. 40, No. 1pp. 221–230

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

Let E = F' where F is a complex Banach space and let π1 : E'' = EF⊥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 PP(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