On quasi-compactness of operator nets on Banach spaces
Tom 203 / 2011
Studia Mathematica 203 (2011), 163-170
MSC: Primary 47A35; Secondary 47B99, 47L05, 47S99.
DOI: 10.4064/sm203-2-3
Streszczenie
The paper introduces a notion of quasi-compact operator net on a Banach space. It is proved that quasi-compactness of a uniform Lotz–Räbiger 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–Räbiger net implies uniform convergence to a finite-rank projection. Precompactness of operator nets is also investigated.
