Extensions Of Derivations on JC-algebras

Extension of a derivation on a universally reversible JC-algebra A⊆B(H)_{sa} to the C*-algebra [A] generated by A in B(H) was studied by Upmier [20, Theorem 2.5]. In this article we study the extension of a Jordan derivation on a universally JC-algebra A to its universal enveloping real and complex C*-algebras R and U, respectively. Also, we establish the relationship between local derivations (resp., 2-local derivations, weak local derivations, weak-2-local derivations) of a universally JC-algebra A and the corresponding maps on its universal enveloping real and complex C*-algebras R and A, respectively.