[Banach] Abstract of a paper by Silvia Lassalle and Pablo Turco

This is an announcement for the paper "The weak bounded approximation property for $\mathcal A$" by Silvia Lassalle and Pablo Turco.

Abstract: Fixed a Banach operator ideal $\mathcal A$, we introduce and investigate the weak bounded approximation property for $\mathcal A$, which is strictly weaker than the bounded approximation property for $\mathcal A$ of Lima, Lima and Oja (2010). We relate the weak BAP for $\mathcal A$ with approximation properties given by tensor norms and show that the metric approximation property of order $p$ of Saphar is the weak BAP for the ideal of $p'$-summing operators, $1<p<\infty$, $\frac 1p + \frac 1{p'}=1$. Under this framework, we address the question of approximation properties passing from $X'$ to $X$ or from $X''$ to $X'$.

Archive classification: math.FA

Mathematics Subject Classification: 47B10, 46A32, 46B28

Remarks: 15 Pages

Submitted from: paturco@dm.uba.ar

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

http://front.math.ucdavis.edu/1410.5670

or

http://arXiv.org/abs/1410.5670