Entire functions uniformly bounded on balls of a Banach space

Volume 204 / 2011

José M. Ansemil, Jerónimo López-Salazar, Socorro Ponte Studia Mathematica 204 (2011), 187-194 MSC: Primary 46G20; Secondary 46E50, 46B99. DOI: 10.4064/sm204-2-5

Abstract

Let $X$ be an infinite-dimensional complex Banach space. Very recently, several results on the existence of entire functions on $X$ bounded on a given ball ${B_{1}\subset X}$ and unbounded on another given ball $B_{2}\subset X$ have been obtained. In this paper we consider the problem of finding entire functions which are uniformly bounded on a collection of balls and unbounded on the balls of some other collection.

Authors

  • José M. AnsemilDepartamento de Análisis Matemático
    Facultad de Matemáticas
    Universidad Complutense de Madrid
    E-28040 Madrid, Spain
    e-mail
  • Jerónimo López-SalazarDepartamento de Análisis Matemático
    Facultad de Matemáticas
    Universidad Complutense de Madrid
    E-28040 Madrid, Spain
    e-mail
  • Socorro PonteDepartamento de Análisis Matemático
    Facultad de Matemáticas
    Universidad Complutense de Madrid
    E-28040 Madrid, Spain
    e-mail

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