This is an announcement for the paper "Strictly singular operators in asymptotic $\ell_p$ Banach spaces" by Anna Pelczar-Barwacz.

Abstract: We present condition on higher order asymptotic behaviour of basic sequences in a Banach space ensuring the existence of bounded non-compact strictly singular operator on a subspace. We apply it in asymptotic $\ell_p$ spaces, $1\leq p<\infty$, in particular in convexified mixed Tsirelson spaces and related asymptotic $\ell_p$ HI spaces.

Archive classification: math.FA

Mathematics Subject Classification: 46B20, 46B06

Remarks: 19 pages

Submitted from: anna.pelczar@im.uj.edu.pl

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

http://front.math.ucdavis.edu/1109.5874

or

http://arXiv.org/abs/1109.5874