Maps on C*-algebras Bi-skew Lie Derivable or Bi-skew Lie Triple Derivable at the Unit

Let B be a unital C*-algebra, A a unital subalgebra of B. We prove that a continuous map φ from A to B is a *-derivation if it is continuous and bi-skew Lie derivable or bi-skew Lie triple derivable at the unit. Moreover, we prove that every bi-skew Lie or bi-skew Lie triple homomorphism at the unit is a Jordan *-homomorphism. © 2024, International Association of Engineers. All rights reserved.