This is an announcement for the paper "Operators on asymptotic $\ell_p$ spaces which are not compact perturbations of a multiple of the identity" by Kevin Beanland.

Abstract: We give sufficient conditions on an asymptotic $\ell_p$ (for $1 < p < \infty$) Banach space which 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 non-compact operators on the HI spaces constructed by G. Androulakis and the author and by I. Deliyanni and A. 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 $X$.

Archive classification: math.FA

The source file(s), SSnonCPT.tex: 51728 bytes, is(are) stored in gzipped form as 0908.1107.gz with size 16kb. The corresponding postcript file has gzipped size 120kb.

Submitted from: kbeanland@gmail.com

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