A Compactness Criterion of Mixed Krasnoselskii-Riesz Type in Regular ideal Spaces of Vector Functions

Abstract

We present a compactness criterion in ideal spaces of vector-valued functions. In the case of real functions, the criterion gives a precise formula for the measure of non-compactness. In the Lebesgue-Bochner spaces $L_p({\mathbb{R}}^n,U)$ the result can be interpreted as a Riesz compactness criterion and generalizes a theorem of Orlicz and Szufla.