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 >