On quasi-compactness of operator nets on Banach spaces

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.

Citation Formats
E. Emelyanov, “On quasi-compactness of operator nets on Banach spaces,” STUDIA MATHEMATICA, vol. 203, no. 2, pp. 163–170, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/37661.