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

The main objective of this research paper consists in introducing the concept of (ψ + , ψ −) -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 (ψ + , ψ −) -derivations defined from a Banach–Jordan pair V = (V + , V −) into a strongly prime Banach–Jordan pair W = (W + , W −)  are automatically continuous under the assumptions that the socle Soc (W) = (Soc (W +) , Soc (W −))  is nonzero and ψ = (ψ + , ψ −)  is an isomorphism from V  into W. Similar results for Banach–Jordan algebras hold to be true. [ABSTRACT FROM AUTHOR]