Entire Functions on Banach Spaces with a Separable Dual

Let E and F be complex Banach spaces. We show that if E has a separable dual, then every holomorphic function from E into F which is bounded on weakly compact sets is bounded on bounded sets.

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Bibliographic Details
Published in:Journal of functional analysis 2002-03, Vol.189 (2), p.496-514
Main Author: Carrión V., Humberto D.
Format: Article
Language:English
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Summary:Let E and F be complex Banach spaces. We show that if E has a separable dual, then every holomorphic function from E into F which is bounded on weakly compact sets is bounded on bounded sets.
ISSN:0022-1236
1096-0783
DOI:10.1006/jfan.2001.3838