Weakly Sequentially Continuous Analytic Functions on a Banach Space

  1. Aron, Richard M.
  2. Herves, Carlos
Libro:
Functional Analysis, Holomorphy and Approximation Theory II

ISSN: 0304-0208

Ano de publicación: 1984

Páxinas: 23-38

Tipo: Capítulo de libro

DOI: 10.1016/S0304-0208(08)70820-X GOOGLE SCHOLAR lock_openAcceso aberto editor

Resumo

Let Hwsc(E) be the space of complex valued analytic functions on the complex Banach space E which map weakly convergent sequences to convergent sequences. Hwsc(E) contains, in general properly, the space Hw(E) of analytic functions on E which are weakly continuous on bounded subsets of E and is, in general, properly contained in the space Hd(E) of analytic functions which are bounded on weakly compact subsets of E. Here we study more closely the relation between these spaces. We show, for example, that for many Banach spaces E, a function f belongs to Hwsc (E) if and only if its differential df belongs to the ε-product Hd(E) ε E'.

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