R. Curto et M. Mathieu, SPECTRALLY BOUNDED GENERALIZED INNER DERIVATIONS, Proceedings of the American Mathematical Society, 123(8), 1995, pp. 2431-2434
We characterize the generalized inner derivations on a unital Banach a
lgebra which are spectrally bounded. In particular, a simplified argum
ent for the recent result due to Bresar that every spectrally bounded
inner derivation maps into the radical is given.