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Summer 2008 Operators on asymptotic $\ell_p$ spaces which are not compact perturbations of a multiple of the identity
Kevin Beanland
Illinois J. Math. 52(2): 515-532 (Summer 2008). DOI: 10.1215/ijm/1248355347

Abstract

We give sufficient conditions on an asymptotic $\ell_p$ (for $1 < p < \infty$) Banach space to ensure the space admits an operator, which is not a compact perturbation of a multiple of the identity. These conditions imply the existence of strictly singular noncompact operators on the HI spaces constructed by G. Androulakis and the author and by Deliyanni and Manoussakis. Additionally, we show that under these same conditions on the space $X$, $\ell_\infty$ embeds isomorphically into the space of bounded linear operators on $X$.

Citation

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Kevin Beanland. "Operators on asymptotic $\ell_p$ spaces which are not compact perturbations of a multiple of the identity." Illinois J. Math. 52 (2) 515 - 532, Summer 2008. https://doi.org/10.1215/ijm/1248355347

Information

Published: Summer 2008
First available in Project Euclid: 23 July 2009

zbMATH: 1185.46005
MathSciNet: MR2524649
Digital Object Identifier: 10.1215/ijm/1248355347

Subjects:
Primary: 46B20
Secondary: 46B03

Rights: Copyright © 2008 University of Illinois at Urbana-Champaign

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Vol.52 • No. 2 • Summer 2008
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