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arXiv · 1403.6431

Bounded holomorphic functions attaining their norms in the bidual

Daniel Carando·Martin Mazzitelli
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Abstract

Under certain hypotheses on the Banach space $X$, we prove that the set of analytic functions in $\mathcal{A}_u(X)$ (the algebra of all holomorphic and uniformly continuous functions in the ball of $X$) whose Aron-Berner extensions attain their norms, is dense in $\mathcal{A}_u(X)$. The result holds also for functions with values in a dual space or in a Banach space with the so-called property $(β)$. For this, we establish first a Lindenstrauss type theorem for continuous polynomials. We also present some counterexamples for the Bishop-Phelps theorem in the analytic and polynomial cases where our results apply.

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Daniel Carando, Martin Mazzitelli. 2015-04-06. Bounded holomorphic functions attaining their norms in the bidual. https://arxiv.org/abs/1403.6431

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