STRONGLY GENERATED BANACH-SPACES AND MEASURES OF NONCOMPACTNESS

To generalize the Hausdorff measure of noncompactness to other classes of bounded sets (like e.g. conditionally weakly compact or Asplund se ts), we introduce Grothendieck classes. We deduce integral inequalitie s for quantities (called Grothendieck measures) related to these class es. As a by-product, we can answer a question concerning the measure o f noncompactness for linear T : X --> Y introduced in [14], and genera lize a theorem about weak solutions of differential equations in Banac h spaces.