0
$\begingroup$

I am unable to find any definition of what rough eigenvalues are. My intuition tells me that this definition only makes sense when we specify some space, say $H$, and suppose we have an operator $O$, and $e_j$ is an operator of $O$.

Then, $e_j$ is a rough eigenvalue of $0$ if the $H$-norm of $e_j$ is not finite?

Am I correct?

Also, it would be very nice if I could have an example to help me understand, if possible.

  • 0
    Can you give us a link to gain more context?2012-08-11
  • 0
    I know what an approximate eigenvalue is, but I can't imagine something called $e_j$ being an eigenvalue, of $O$, 0, or anything else. Do please elaborate.2012-08-11
  • 0
    It seems that "$e_j$ is a rough eigenvalue of $0$" should read "$e_j$ *has* a rough eigenvalue of $0$"?2012-08-11
  • 0
    Ah, yes. Even so, I have no idea what a rough or approximate eigenvalue of 0 would have to do with an operator being unbounded. Maybe an approximate eigenvalue of $\infty$.2012-08-11

0 Answers 0