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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
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E. Emelyanov, “On quasi-compactness of operator nets on Banach spaces,”
STUDIA MATHEMATICA
, pp. 163–170, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/37661.