[Banach] Abstract of a paper by Alistair Bird, Graham Jameson and Niels Jakob Laustsen

This is an announcement for the paper "The Giesy--James theorem for general index $p$, with an application to operator ideals on the $p$th James space" by Alistair Bird, Graham Jameson and Niels Jakob Laustsen.

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 $(\ell_\infty^1 \oplus \ell_\infty^2 \oplus \cdots \oplus \ell_\infty^n \oplus \cdots)_{\ell_p}$ of $J_p$.

Archive classification: math.FA math.OA

Mathematics Subject Classification: 46B45, 47L20 (Primary) 46B07, 46H10, 47L10 (Secondary)

Remarks: 16 pages

Submitted from: alistairbird@gmail.com

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

http://front.math.ucdavis.edu/1109.1776

or

http://arXiv.org/abs/1109.1776