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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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    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

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