Absolutely \(p\)-summable sequences in Banach spaces and range of vector measures
The author studies the question, given \(1 \leq p<\infty\), for what Banach spaces \(X\) every \(p\)-summable sequence of elements of \(X\) (i.e., a sequence \((x_i)\) in \(X\) with \(\sum_i \|x_i\|^p < \infty\)) is contained in the range of some \(X\)-valued measure. Most of the results establish necessary and sufficient conditions on \(X\) to have properties of such kind in terms of \((p,q)\)-absolutely summing operators from \(X\) to \(\ell_1\). Besides, some examples and open problems are given.
scientific article; zbMATH DE number 5541254
scientific article