Strictly singular operators in asymptotic $\ell_p$ Banach spaces

Details Strictly singular operators in asymptotic $\ell_p$ Banach spaces Strictly singular operators in asymptotic $\ell_p$ Banach spaces

2011-09-27

arxiv.org/abs/1109.5874v1

Mathematics

Functional Analysis

19 pages

Scientific paper

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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