info:eu-repo/semantics/article
On the polynomial lindenstrauss theorem
Fecha
2012-10Registro en:
Carando, Daniel Germán; Lassalle, Silvia Beatriz; Mazzitelli, Martin Diego; On the polynomial lindenstrauss theorem; Academic Press Inc Elsevier Science; Journal of Functional Analysis; 263; 7; 10-2012; 1809-1824
0022-1236
CONICET Digital
CONICET
Autor
Carando, Daniel Germán
Lassalle, Silvia Beatriz
Mazzitelli, Martin Diego
Resumen
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 Bollobás, of these results.