On quasi-compactness of operator nets on Banach spaces

Eduard Yu. Emel'yanov. "On quasi-compactness of operator nets on Banach spaces." Studia Mathematica 203.2 (2011): 163-170. <http://eudml.org/doc/285862>.

@article{EduardYu2011,
abstract = {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.},
author = {Eduard Yu. Emel'yanov},
journal = {Studia Mathematica},
keywords = {operator net; quasi-compactness; U LR-net; uniform convergence; precompactness},
language = {eng},
number = {2},
pages = {163-170},
title = {On quasi-compactness of operator nets on Banach spaces},
url = {http://eudml.org/doc/285862},
volume = {203},
year = {2011},
}

TY - JOUR
AU - Eduard Yu. Emel'yanov
TI - On quasi-compactness of operator nets on Banach spaces
JO - Studia Mathematica
PY - 2011
VL - 203
IS - 2
SP - 163
EP - 170
AB - 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.
LA - eng
KW - operator net; quasi-compactness; U LR-net; uniform convergence; precompactness
UR - http://eudml.org/doc/285862
ER -