On the essential numerical range of a generalized derivation
Bojan Magajna · Proceedings of the American Mathematical Society · 1987
Let A A and B B be bounded operators on Hilbert spaces H \mathcal {H} and L \mathcal {L} , respectively. The essential numerical range of the operator X → A X − X B X \to AX - XB , defined on the Hilbert-Schmidt class C 2 ( L , H ) {\mathcal {C}^2}\left ( {\mathcal {L},\mathcal {H}} \right ) is expressed in terms of the numerical and the essential numerical ranges of A A and B B .