Similarity orbits and the range of the generalized derivation $X\to MX-XN$
Similarity orbits and the range of the generalized derivation $X\to MX-XN$
If $M$ and $N$ are bounded operators on infinite dimensional complex Hilbert spaces $\mathcal {H}$ and $\mathcal {K}$, let $\tau (X) = MX - XN$ for $X$ in $\mathcal {L}(\mathcal {K},\mathcal {H})$. The closure of the range of $\tau$ is characterized when $M$ and $N$ are normal. There is a …