Tensorial Representations of Positive Weakly (q,r)-Dominated Multilinear Operators

Document Type : Original Article

Authors

Adel Bounabab ¹

Abdelaziz Belaada ¹

Athmane Ferradi ²

Khalil Saadi ¹

¹ Laboratory of Functional Analysis and Geometry of Spaces, Faculty of Mathematics and Computer Science‎, ‎University of Mohamed Boudiaf-M'sila‎, ‎Po Box 166‎, ‎Ichebilia‎, ‎28000‎, ‎M'sila‎, ‎Algeria

² Department of Mathematics‎, ‎\'{E}cole Normale Sup\'{e}rieure de Bousa\^{a}da‎, ‎28001 Bousaada‎, ‎Algeria

10.22067/kjm.2026.548319.3684

Abstract

We introduce the class of positive weakly (q,r)-dominated multilinear operators between Banach lattices. This notion extends classical domination and summability concepts to the positive multilinear setting and generates a new positive multi-ideal. A Pietsch domination theorem and a polynomial version are established. Finally, we provide a tensorial representation that yields an isometric identification with the dual of an appropriate completed tensor product.

Keywords

Banach lattice

Positive multilinear ideal

Positive weakly (q

r)-dominated operators

Tensional representation

Subjects

• 47 Operator theory

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