Characterizations of all-derivable points in B(H).

Letandbe two Hilbert spaces, and letbe the algebra of all bounded linear operators frominto. We say that an elementis an all-derivable point inif every derivable linear mappingat(i.e.for anywith) is a derivation. Let bothandbe two linear mappings. In this paper, the following result will be proved : iffor anyand, thenandfor some. As an important application, we will show that an operatoris an all-derivable point inif and only if. [ABSTRACT FROM AUTHOR]