This is an announcement for the paper "On the polynomial Lindenstrauss theorem" by Daniel Carando, Silvia Lassalle and Martin Mazzitelli.
Abstract: Under certain hypotheses on the Banach space $X$, we show that the set of $N$-homogeneous polynomials from $X$ to any dual space, whose Aron-Berner extensions are norm attaining, is dense in the space of all continuous $N$-homogeneous polynomials. To this end we prove an integral formula for the duality between tensor products and polynomials. We also exhibit examples of Lorentz sequence spaces for which there is no polynomial Bishop-Phelps theorem, but our results apply. Finally we address quantitative versions, in the sense of Bollob'as, of these results.
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/1206.3218
or