Resumen de Schreier singular operators

Alexey I. Popov

• In this paper we further investigate recently introduced Schreier singular operators. We show that the class of Schreier singular operators is stable under left and right multiplication by bounded operators. We also present a characterization of Schreier singular operators in terms of spreading models.

  Androulakis, Dodos, Sirotkin, and Troitsky (Israel J. Math, to appear) showed that under cerain conditions on the space the product of sufficiently many Schreier singular operators is compact. We extend this result to a broader class of spaces. Finally, we show that this cannot be extended to arbitrary Banach spaces by presenting an example of a finitely strictly singular operator which is not even polynomially compact.