Multiple tensor norms of Michor's type and associated operator ideals. In honour of Manuel López-Pellicer (Q2337497)

This is mainly a careful elaboration of the author's interesting article [Positivity 22, No. 4, 1109--1142 (2018; Zbl 1416.46069)]. Michor's tensor norm \(\alpha^C_{\pmb{r}}\) on \((n+1)\)-fold tensor products of Banach spaces leads to \(\alpha^C_{\pmb{r}}\)-integral multilinear operators \(T: \prod_{j=1}^n E_j \to E_{n+1}\) in Banach spaces (in the sense of Grothendieck's famous Résumé). The main result of the above article, with a proof which is a real tour de force, characterizes these multilinear operators in terms of a natural factorization theorem within \(L_p\)-spaces. For the entire collection see [Zbl 1419.46002].