Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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.

share|improve this question
    
Can you give us a link to gain more context? –  Ravi Donepudi 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

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.