5
$\begingroup$

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!

  • 0
    If you don't have access to MathSciNet, try this Google Scholar search: http://scholar.google.com/scholar?q=operator+similarity+author%3ADA+author%3Aherrero&btnG=&hl=en&as_sdt=0%2C16. There are several relevant looking articles freely available in pdf format.2012-07-01

1 Answers 1

2

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.