On quasi-compactness of operator nets on Banach spaces

EMELYANOV E.

STUDIA MATHEMATICA, cilt.203, sa.2, ss.163-170, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 203 Sayı: 2
  • Basım Tarihi: 2011
  • Doi Numarası: 10.4064/sm203-2-3
  • Dergi Adı: STUDIA MATHEMATICA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.163-170
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.