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arXiv · 1109.1776

The Giesy--James theorem for general index $p$, with an application to operator ideals on the $p$th James space

Alistair Bird·Graham Jameson·Niels Jakob Laustsen
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Abstract

A theorem of Giesy and James states that $c_0$ is finitely representable in James' quasi-reflexive Banach space $J_2$. We extend this theorem to the $p$th quasi-reflexive James space $J_p$ for each $p \in (1,\infty)$. As an application, we obtain a new closed ideal of operators on $J_p$, namely the closure of the set of operators that factor through the complemented subspace $(\ell_\infty^1 \oplus \ell_\infty^2 \oplus...\oplus \ell_\infty^n \oplus...)_{\ell_p}$ of $J_p$.

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Alistair Bird, Graham Jameson, Niels Jakob Laustsen. 2011-09-08. The Giesy--James theorem for general index $p$, with an application to operator ideals on the $p$th James space. https://arxiv.org/abs/1109.1776

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