Resumen de Approximately local derivations

Ebrahim Samei

• Certain linear operators from a Banach algebra into a Banach -bimodule , which are called approximately local derivations, are studied. It is shown that when is a -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 into are derivations. This, in particular, extends a result of B. E. Johnson that 'local derivations on -algebras are derivations' and provides an alternative proof of it.