Geometric characterizations and Banach-Steinhaus theorem for multilinear multivalued maps

Document Type : Original Article

Authors

Khaled Bouadjila ¹

Elhadj Dahia ²

¹ ‎Laboratoire d'Analyse Fonctionnelle et G\'{e}om\'{e}trie des Espaces‎, ‎University of M'sila‎, ‎M'sila 28000‎, ‎Algeria

² Faculty of Science‎, ‎Department of Mathematics and Computer Science‎, ‎Yahia Feres University‎ - ‎Medea‎, ‎Medea 26000‎, ‎Algeria

10.22034/kjm.2025.487707.3366

Abstract

We introduce and investigate a new concept of bounded multilinear relations between normed spaces, highlighting some algebraic properties of this new class of multivalued mappings. We characterize the norm of a bounded multilinear relation, thereby, obtaining an important geometric characterization of these mappings. As an application, we prove the Uniform boundedness principle in the framework of multilinear relations on Banach spaces.

Keywords

Multilinear relations

multivalued linear operators

Banach-Steinhaus theorem

Subjects

• 46 Functional analysis

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