A characterization of strongly weakly compactly generated Banach space
A Banach space \(X\) is called strongly WCG if \(X\) contains a weakly compact subset \(K\) which almost absorbs any other weakly compact subset \(L\), i.e., for every \(\varepsilon>0\) there is \(n\) so that \(L\subset nK+\varepsilon B_X\). The author proves that for a strongly WCG space \(X\) there exists a reflexive space \(R\) and a continuous linear operator \(T:R\to X\) such that \(T(B_R)\) almost absorbs every weakly compact set. This result is analogous to the well-known Davis--Figiel--Johnson--Pełczyński factorization theorem and the proof is similar.
Davis--Figiel--Johnson--Pełczyński factorisation
scientific article; zbMATH DE number 2143239