On quasi-compactness of operator nets on Banach spaces

EMELYANOV E.

STUDIA MATHEMATICA, vol.203, no.2, pp.163-170, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 203 Issue: 2
  • Publication Date: 2011
  • Doi Number: 10.4064/sm203-2-3
  • Journal Name: STUDIA MATHEMATICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.163-170
  • Middle East Technical University Affiliated: Yes

Abstract

The paper introduces a notion of quasi-compact operator net on a Banach space. It is proved that quasi-compactness of a uniform Lotz-Rabiger net (T(lambda))(lambda) is equivalent to quasi-compactness of some operator T(lambda). We prove that strong convergence of a quasi-compact uniform Lotz-Rabiger net implies uniform convergence to a finite-rank projection. Precompactness of operator nets is also investigated.