Multiple tensor norms of Michor’s type and associated operator ideals. In honour of Manuel López-Pellicer. (English) Zbl 1442.46057
Ferrando, Juan Carlos (ed.), Descriptive topology and functional analysis. II. In honour of Manuel López-Pellicer mathematical work. Proceedings of the 2nd meeting in topology and functional analysis, Elche, Spain, June 7–8, 2018. Cham: Springer. Springer Proc. Math. Stat. 286, 191-224 (2019).
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].
For the entire collection see [Zbl 1419.46002].
Reviewer: Andreas Defant (Oldenburg)
MSC:
| 46M05 | Tensor products in functional analysis |
| 47L20 | Operator ideals |
| 46G25 | (Spaces of) multilinear mappings, polynomials |
