This is an announcement for the paper "Constructing Banach ideals using upper $\ell_p$-estimates" by Ben Wallis.

Abstract: Using upper $\ell_p$-estimates for normalized weakly null sequence images, we describe a new family of operator ideals $\mathcal{WD}_{\ell_p}^{(\infty,\xi)}$ with parameters $1\leq p\leq\infty$ and $1\leq\xi\leq\omega_1$. These classes contain the completely continuous operators, and are distinct for all choices $1\leq p\leq\infty$ and, when $p\neq 1$, for all choices $\xi\neq\omega_1$. For the case $\xi=1$, there exists an ideal norm $|\cdot|_{(p,1)}$ on the class $\mathcal{WD}_{\ell_p}^{(\infty,1)}$ under which it forms a Banach ideal.

Archive classification: math.FA

Mathematics Subject Classification: 47L20, 46B45, 46A45, 46B25

Submitted from: wallis@math.niu.edu

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

http://front.math.ucdavis.edu/1407.5948

or

http://arXiv.org/abs/1407.5948