Entire functions on c0
Copyright policy )Entire functions on c0
It is shown that every holomorphic function on the Banach space \(c_ 0\) of complex null sequences which is bounded on weakly compact subsets is bounded on bounded subsets of \(c_ 0\). This result answers a question of \textit{R. M. Aron, C. Hérves, M. Valdivia} [J. Funct. Anal. 52, 189-204 (1983; Zbl 0517.46019)] in the negative. The result also shows that a holomorphic analogue of the following characterization of reflexive Banach spaces does not hold: A Banach space E is reflexive if and only if every weakly continuous function on E is bounded on bounded subsets of E [cf. \textit{M. Valdivia}, J. Funct. Anal. 24, 1-10 (1977; Zbl 0344.46004)].
- University College Dublin Ireland
Duality and reflexivity in normed linear and Banach spaces, Entire functions of several complex variables, Infinite-dimensional holomorphy, Sequence spaces (including Köthe sequence spaces), Analysis
Duality and reflexivity in normed linear and Banach spaces, Entire functions of several complex variables, Infinite-dimensional holomorphy, Sequence spaces (including Köthe sequence spaces), Analysis
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