On derivable mappings (Q601328)

In this paper, the authors firstly explore some relations between derivable mappings and algebraic Jordan derivations and give some properties of algebraic Jordan derivations needed to prove the main results. After this, they show that if \(\mathcal A\) is a canonical subalgebra of a unital \(AF C^*\)- algebra \(\mathcal B\) and \(\delta\) is a bounded linear mapping from \(\mathcal A\) into \(\mathcal B\) such that \(\delta\) is derivable at \(I\), then \(\delta\) is a derivation. Also, they show that every bounded local derivation from a canonical subalgebra \(\mathcal A\) of a unital \(AF C^*\) -algebra \(\mathcal B\) into a unital Banach \(\mathcal A\)-bimodule is a derivation.