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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.

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Can you give us a link to gain more context? – Ravi Aug 11 '12 at 4:53
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. – Kevin Carlson Aug 11 '12 at 5:02
It seems that "$e_j$ is a rough eigenvalue of $0$" should read "$e_j$ has a rough eigenvalue of $0$"? – joriki Aug 11 '12 at 5:05
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 $\infty$. – Kevin Carlson Aug 11 '12 at 8:11

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