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Entire Functions on Banach Spaces with a Separable Dual

✍ Scribed by Humberto D. Carrión V.

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
153 KB
Volume
189
Category
Article
ISSN
0022-1236

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✦ Synopsis

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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This paper shows that every w\*-lower semicontinuous Lipschitzian convex function on the dual of a locally uniformly convexifiable Banach space, in particular, the dual of a separable Banach space, can be uniformly approximated by a generically Fréchet differentiable w\*-lower semicontinuous monoton