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Winter 2013 Strictly singular operators in Tsirelson like spaces
Spiros A. Argyros, Kevin Beanland, Pavlos Motakis
Illinois J. Math. 57(4): 1173-1217 (Winter 2013). DOI: 10.1215/ijm/1417442566

Abstract

For each $n\in \mathbb{N} $ a Banach space $\mathfrak{X}_{_{^{0,1}}}^{n}$ is constructed having the property that every normalized weakly null sequence generates either a $c_{0}$ or $\ell_{1}$ spreading models and every subspace has weakly null sequences generating both $c_{0}$ and $\ell_{1}$ spreading models. The space $\mathfrak{X}_{_{^{0,1}}}^{n}$ is also quasiminimal and for every infinite dimensional closed subspace $Y$ of $\mathfrak{X}_{_{^{0,1}}}^{n}$, for every $S_{1},S_{2},\ldots,S_{n+1}$ strictly singular operators on $Y$, the operator $S_{1}S_{2}\cdots S_{n+1}$ is compact. Moreover, for every subspace $Y$ as above, there exist $S_{1},S_{2},\ldots,S_{n}$ strictly singular operators on $Y$, such that the operator $S_{1}S_{2}\cdots S_{n}$ is non-compact.

Citation

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Spiros A. Argyros. Kevin Beanland. Pavlos Motakis. "Strictly singular operators in Tsirelson like spaces." Illinois J. Math. 57 (4) 1173 - 1217, Winter 2013. https://doi.org/10.1215/ijm/1417442566

Information

Published: Winter 2013
First available in Project Euclid: 1 December 2014

zbMATH: 1315.46008
MathSciNet: MR3285871
Digital Object Identifier: 10.1215/ijm/1417442566

Subjects:
Primary: 46B03, 46B06, 46B25, 46B45, 47A15

Rights: Copyright © 2013 University of Illinois at Urbana-Champaign

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Vol.57 • No. 4 • Winter 2013
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