Publications of the Research Institute for Mathematical Sciences


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Volume 45, Issue 2, 2009, pp. 383–391
DOI: 10.2977/prims/1241553124

Representation of Spaces of Entire Functions on Banach Spaces

José M. Ansemil[1], Richard M. Aron[2] and Socorro Ponte[3]

(1) Departamento de Análisis Matemático, Universidad Complutense de Madrid, Avda. Complutense s/n, 28040, MADRID, SPAIN
(2) Department of Mathematical Sciences, Kent State University, OH 44242, KENT, UNITED STATES
(3) Departamento de Análisis Matemático, Universidad Complutense de Madrid, Avda. Complutense s/n, 28040, MADRID, SPAIN

We prove the impossibility of expressing the space of entire functions on any infinite dimensional complex Banach space with a Schauder basis E as a countable union of spaces of entire functions that are bounded on countable open covers of E.

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Ansemil José, Aron Richard, Ponte Socorro: Representation of Spaces of Entire Functions on Banach Spaces. Publ. Res. Inst. Math. Sci. 45 (2009), 383-391. doi: 10.2977/prims/1241553124