TITLE: References on similarity orbits of operators
QUESTION [6 upvotes]: Given an operator $T\in\mathcal{L}(\mathcal{H})$, where $\mathcal{H}$ is a separable Hilbert space, the similarity orbit of $T$ is defined by \begin{equation}
SO(T)=\{STS^{-1}:S\in\mathcal{L}(\mathcal{H})\}.
\end{equation} 
I read about this theory in some papers but I wonder whether there is some good books discussing this issue systematically. I am particularly interested in properties like what is the infimum of norm of operators in $SO(T)$ and how far is the orbit from diagonal operators? compact operators? finite rank operators?
Thanks!

REPLY [3 votes]: I really want to close this problem. As mentioned by user6299 in his/her comment, Herrero has done a lot of work on problems related to orbits of operators in Hilbert spaces. Also a good referece (but quite hard) is his book Approximation of Hilbert Space Operators.