Strictly singular operators in asymptotic $\ell_p$ Banach spaces

Anna Pelczar-Barwacz

Strictly singular operators in asymptotic $\ell_p$ Banach spaces

Functional Analysis 2011-09-28 v1

Authors: 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.

Keywords

strictly singular operators asymptotic ell_p spaces Banach spaces Tsirelson spaces HI spaces basic sequences

Cite

@article{arxiv.1109.5874,
  title  = {Strictly singular operators in asymptotic $\ell_p$ Banach spaces},
  author = {Anna Pelczar-Barwacz},
  journal= {arXiv preprint arXiv:1109.5874},
  year   = {2011}
}

Comments

19 pages

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