On quasi-compactness of operator nets on Banach spaces

Eduard Yu. Emel'yanov

Studia Mathematica, Tome 204 (2011), p. 163-170 / Harvested from The Polish Digital Mathematics Library

Résumé

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 ${(T_{λ})}_{λ}$ is equivalent to quasi-compactness of some operator $T_{λ}$ . 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.

Publié le : 2011-01-01

Zbl 1232.47010

EUDML-ID : urn:eudml:doc:285862

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     title = {On quasi-compactness of operator nets on Banach spaces},
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     year = {2011},
     pages = {163-170},
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Eduard Yu. Emel'yanov. On quasi-compactness of operator nets on Banach spaces. Studia Mathematica, Tome 204 (2011) pp. 163-170. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm203-2-3/