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arXiv · 1407.5948

Constructing Banach ideals using upper $\ell_p$-estimates

Ben Wallis
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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.

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Ben Wallis. 2014-07-22. Constructing Banach ideals using upper $\ell_p$-estimates. https://arxiv.org/abs/1407.5948

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