Closed injective ideals of multilinear operators, related measures and interpolation

[EN] We introduce and discuss several ways of extending the inner measure arisen from the closed injective hull of an ideal of linear operators to the multilinear case. In particular, we consider new measures that allow to characterize the operators that belong to a closed injective ideal of multilinear operators as those having measure equal to zero. Some interpolation formulas for these measures, and consequently interpolation results involving ideals of multilinear operators, are established. Examples and applications related to summing multilinear operators are also shown.

This is the peer reviewed version of the following article: Manzano, A, Rueda, P, Sánchez-Pérez, EA. Closed injective ideals of multilinear operators, related measures and interpolation. Mathematische Nachrichten. 2020; 293: 510-532, which has been published in final form at https://doi.org/10.1002/mana.201800415. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.