This is an announcement for the paper "Bounded holomorphic functions attaining their norms in the bidual" by Daniel Carando and Martin Mazzitelli.

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 $(\beta)$. 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.

Archive classification: math.FA

Submitted from: mmazzite@dm.uba.ar

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1403.6431

or

http://arXiv.org/abs/1403.6431