Bounded Holomorphic Functions Attaining their Norms in the Bidual
Daniel Carando
Universidad de Buenos Aires, ArgentinaMartin Mazzitelli
Universidad de Buenos Aires, Argentina
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Abstract
Under certain hypotheses on the Banach space , we prove that the set of analytic functions in (the algebra of all holomorphic and uniformly continuous functions in the ball of ) whose Aron–Berner extensions attain their norms is dense in . This Lindenstrauss type result also holds for functions with values in a dual space or in a Banach space with the so-called property (). We show that the Bishop–Phelps theorem does not hold for for a certain Banach space , while our Lindenstrauss theorem does. In order to obtain our results, we first handle their polynomial cases.
Cite this article
Daniel Carando, Martin Mazzitelli, Bounded Holomorphic Functions Attaining their Norms in the Bidual. Publ. Res. Inst. Math. Sci. 51 (2015), no. 3, pp. 489–512
DOI 10.4171/PRIMS/162