This is an announcement for the paper "A general abstract approach to approximation properties in Banach" by Sonia Berrios and Geraldo Botelho.

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.

Archive classification: math.FA

Submitted from: botelho@ufu.br

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1307.8073

or

http://arXiv.org/abs/1307.8073