Ideals of multilinear mappings via Orlicz spaces and translation invariant operators

[EN] We study some new summability properties of multilinear operators. We introduce the concepts of phi-summing, phi semi-integral and phi-dominated multilinear maps generated by Orlicz functions. We prove a variant of Pietsch's domination theorem for phi-summing operators, providing also a characterization of phi-dominated operators in terms of factorizations. We analyze vector-valued inequalities associated to these maps, which are applied to obtain general variants of multiple summing operators. We also study translation invariant multilinear operators acting in products of spaces of continuous functions, proving that a factorization theorem can be obtained for them as a consequence of a suitable representation of the corresponding normalized Haar measure.

This is the peer reviewed version of the following article: Mastylo, M, Sánchez Pérez, EA. Ideals of multilinear mappings via Orlicz spaces and translation invariant operators. Mathematische Nachrichten. 2021; 294: 959-976, which has been published in final form at https://doi.org/10.1002/mana.201900380. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.