Multilinear extensions of absolutely \((p;q;r)\)-summing operators
The author introduces and explores the notion of absolutely \(\left( p;q_{1},\dots,q_{m};r\right) \)-summing multilinear operators. When \(r=\infty\) the well-known case of absolutely \(\left( p;q_{1},\dots,q_{m}\right) \)-summing multilinear operators is recovered. Among several interesting results, a Pietsch domination-type theorem is proved. The proof uses a general technique introduced by the reviewer, \textit{J. Santos} and \textit{J. B. Seoane-Sepúlveda} [Adv. Math. 229, No. 2, 1235--1265 (2012; Zbl 1248.47024)]. A factorization theorem and connections with the class of Cohen strongly \(p\)-summing multilinear operators are also presented.
absolutely summing multilinear operators
scientific article; zbMATH DE number 6004389
scientific article