On quasi-compactness of operator nets on Banach spaces
STUDIA MATHEMATICA, cilt.203, sa.2, ss.163-170, 2011 (SCI-Expanded, Scopus)
- 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.