A note on (ψ+,ψ−)-derivations of Banach–Jordan systems with nonzero socle

Abstract

The main objective of this research paper consists in introducing the concept of [Formula: see text]-derivations acting on Banach–Jordan pairs and Banach–Jordan algebras and giving an automatic continuity result of the operators in question under some algebraic conditions. Concretely, we prove that [Formula: see text]-derivations defined from a Banach–Jordan pair [Formula: see text] into a strongly prime Banach–Jordan pair [Formula: see text] are automatically continuous under the assumptions that the socle [Formula: see text] is nonzero and [Formula: see text] is an isomorphism from [Formula: see text] into [Formula: see text]. Similar results for Banach–Jordan algebras hold to be true.