Mappings between Banach spaces that send mixed summable sequences into absolutely summable sequences
This paper deals with a generalization of the notion of \((p,q)\)-summing operators on a Banach space that was introduced by Pietsch and studied by him and numerous others many years ago. The definitions as well as the results obtained are highly technical and consequently will not be summarized here. A quote from the author's abstract will suffice to indicate the nature and direction of the work. ``We study mappings from an open subset \(A\) of a Banach space \(E\) into another Banach space \(F\) such that, once \(a\) in \(A\) is fixed, for mixed \((s;q)\)-summable sequences \(\{x(j)\}\) of elements of a fixed neighborhood of \(0\) in \(E\), the sequence \(\{f(a+ x(j))- f(a)\}\) is absolutely \(p\)-summable in \(F\).''
scientific article; zbMATH DE number 2107223