Abstract. In [11, Theorem 3.2], P. J. Maher has shown that, if $N$ is normal and $T\in{\rm Ker}(\delta_N|C_p)$, then $\| T-\delta_N(X) \|_p\ge\| T\|_p$ for any $X\in L(H)$. In the first part, we generalize P. J. Maher's results. We also generalize P. J. Maher's results by minimizing the map $X\to\| T-(AX-XB)\|_p^p$, $1\le p< \infty$ and classifying its critical points.

AMS Subject Classification (1991): 47B47, 47B10

Keyword(s): commutator approximation, generalized derivation, Fuglede-Putnam theorem

Received March 30, 1995 and in revised form April 3, 1996. (Registered under 6114/2009.)