Reflexivity of Spaces of Polynomials on Direct Sums of Banach Spaces

  • Adriano L. Aguiar

    Maceió, Brazil
  • Luiza A. Moraes

    Universidade Federal do Rio de Janeiro, Brazil

Abstract

Let be the space of the continuous -homogeneous polynomials from into and be the space of the holomorphic mappings from into that are bounded in the bounded subsets of , both spaces endowed with the topology of uniform convergence on the bounded subsets of . The reflexivity of is studied in connection with the density of the space of the finite type -homogeneous polynomials in and in connection with the equality in case is a reflexive countable direct sum of complex Banach spaces and is a reflexive complex Banach space. The reflexivity of is also considered.

Cite this article

Adriano L. Aguiar, Luiza A. Moraes, Reflexivity of Spaces of Polynomials on Direct Sums of Banach Spaces. Publ. Res. Inst. Math. Sci. 45 (2009), no. 2, pp. 351–361

DOI 10.2977/PRIMS/1241553122