On quasi-compactness of operator nets on Banach spaces

Date

2011-01-01

Author

Emelyanov, Eduard

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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.

Subject Keywords

General Mathematics

URI

https://hdl.handle.net/11511/37661

Journal

STUDIA MATHEMATICA

DOI

https://doi.org/10.4064/sm203-2-3

Collections

Department of Mathematics, Article

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.