Abstract :
Certain linear operators from a Banach algebra A into a Banach A-bimodule X, which are called
approximately local derivations, are studied. It is shown that when A is a C∗-algebra, a Banach
algebra generated by idempotents, a semisimple annihilator Banach algebra, or the group algebra
of a SIN or a totally disconnected group, bounded approximately local derivations from A into X
are derivations. This, in particular, extends a result of B. E. Johnson that ‘local derivations on
C∗-algebras are derivations’ and provides an alternative proof of it.
