An announcement concerning my preliminary communication “A class of Kreiss-type uniformly bounded systems of operators”
We prove a fixed point theorem for Borsuk continuous mappings with spherical values, which extends a previous result. We apply some nonstandard properties of the Stiefel-Whitney classes.
Given an operator ideal , we say that a Banach space X has the approximation property with respect to if T belongs to for every Banach space Y and every T ∈ (Y,X), being the topology of uniform convergence on compact sets. We present several characterizations of this type of approximation property. It is shown that some of the existing approximation properties in the literature may be included in this setting.