Timeline for Invertible operator with countable spectrum
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Aug 21, 2014 at 6:17 | review | Suggested edits | |||
| Aug 21, 2014 at 6:28 | |||||
| Aug 19, 2014 at 19:29 | vote | accept | Ali Taghavi | ||
| Aug 19, 2014 at 19:29 | comment | added | Ali Taghavi | Thank you very much for your beautiful answer and your reference to Putnam theorem. However, regarding the eigenvalue problem, i think that $I+V$ is a counter example where $V$ is the Voltra integral operator. It has a single spectrum $\{1\}$ which is not eigenvalue. | |
| Aug 19, 2014 at 16:37 | comment | added | Mike Jury | OK, I no longer trust my claim about eigenvalues; however it is true that if 0 is in the boundary of the spectrum of a Fredholm operator (which is of course the case here), then it must be isolated and the operator must have index 0. This follows from a theorem of Putnam; see Conway's "A Course in Functional Analysis", Theorems XI.6.8 and XI.6.9. | |
| Aug 19, 2014 at 16:26 | comment | added | Mike Jury | I thought this should just follow from the Fredholm assumption and the Riesz functional calculus, but perhaps it is more subtle than that. Let me think about it some more. | |
| Aug 19, 2014 at 16:09 | comment | added | Ali Taghavi | thank you very much for your interesting answer. I have a question on your statement "Isolated points are eigenvalue" In this statement, is not necessary that we assume T is normal? | |
| Aug 19, 2014 at 15:30 | history | edited | Mike Jury | CC BY-SA 3.0 |
added 679 characters in body
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| Aug 19, 2014 at 13:00 | history | answered | Mike Jury | CC BY-SA 3.0 |