Abstract
We propose a unifying approach to numerous approximation properties in Banach spaces studied from the 1930s up to our days. To do so, we introduce the concept of ideal topology and 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 ideal topology tau, by operators belonging to the operator ideal J. 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 general framework.
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