A compactness criterion of mixed Krasnoselskiĭ-Riesz type in regular ideal spaces of vector functions
There is given a compactness criterion in ideal spaces (Banach function spaces) of vector-valued functions \(f\) on a measure space \(S\), with values in a Banach space \(U\). It follows from some estimates between measures of non-compactness \(\alpha\) of Kuratowski, \(\chi_Y\) by Hausdorff, \(\chi_i=\) inner Hausdorff measure of non-compactness, and a measure \(\omega\). If \(X\) is a regular preideal space (Köthe space) of functions \(f: S\to U\), where \(U\) is finite-dimensional, from these estimates follow necessary and sufficient conditions in order that \(M\subset X\) be precompact.
scientific article; zbMATH DE number 1356405
scientific article