On quasi-compactness of operator nets on Banach spaces
Studia Mathematica, Tome 203 (2011) no. 2, pp. 163-170
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
paper introduces notion quasi compact operator net banach space proved quasi compactness uniform lotz biger net lambda lambda equivalent quasi compactness operator lambda prove strong convergence quasi compact uniform lotz biger net implies uniform convergence finite rank projection precompactness operator nets investigated
Affiliations des auteurs :
Eduard Yu. Emel'yanov 1
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author = {Eduard Yu. Emel'yanov},
title = {On quasi-compactness of operator nets on {Banach} spaces},
journal = {Studia Mathematica},
pages = {163--170},
publisher = {mathdoc},
volume = {203},
number = {2},
year = {2011},
doi = {10.4064/sm203-2-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm203-2-3/}
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Eduard Yu. Emel'yanov. On quasi-compactness of operator nets on Banach spaces. Studia Mathematica, Tome 203 (2011) no. 2, pp. 163-170. doi: 10.4064/sm203-2-3
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