On the polynomial Lindenstrauss theorem
Functional Analysis
2013-04-23 v1
Abstract
Under certain hypotheses on the Banach space , we show that the set of -homogeneous polynomials from to any dual space, whose Aron-Berner extensions are norm attaining, is dense in the space of all continuous -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.
Cite
@article{arxiv.1206.3218,
title = {On the polynomial Lindenstrauss theorem},
author = {Daniel Carando and Silvia Lassalle and Martín Mazzitelli},
journal= {arXiv preprint arXiv:1206.3218},
year = {2013}
}