Continuity of deriations of Banach-Lie algebras

In his monograph of 1972, P. De La Harpe proved the continuity of the derivations of the classical Banach-Lie algebras of compact operators on Hilbert spaces. In this note an elementary proof of this result is provided by using only the algebraic fact that these Banach-Lie algebras are strongly prime and contain extremal elements.

A. Fernández López < emalfer@agt.cie.uma.es >