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Strictly singular operators in asymptotic $\ell_p$ Banach spaces

Published 27 Sep 2011 in math.FA | (1109.5874v1)

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.

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Authors (1)

  1. Anna Pelczar-Barwacz 

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