A general abstract approach to approximation properties in Banach spaces
Functional Analysis
2013-07-31 v1
Abstract
We propose a unifying approach to many approximation properties studied in the literature from the 1930s up to our days. To do so, we say that a Banach space E has the (I,J,{\tau})-approximation property if E-valued operators belonging to the operator ideal I can be approximated, with respect to the topology {\tau}, by operators belonging to the operator ideal J. Restricting {\tau} to a class of linear topologies, which we call ideal topologies, this concept recovers many classical/recent approximation properties as particular instances and several important known results are particular cases of more general results that are valid in this abstract framework.
Cite
@article{arxiv.1307.8073,
title = {A general abstract approach to approximation properties in Banach spaces},
author = {Sonia Berrios and Geraldo Botelho},
journal= {arXiv preprint arXiv:1307.8073},
year = {2013}
}