Timeline for cokernels of semi-Fredholm operators
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Oct 19, 2011 at 0:08 | comment | added | Bill Johnson | Yes, that is right. | |
| Oct 18, 2011 at 20:42 | comment | added | Orbicular | @Bill: I know, but that was not the question. The question was whether one can always identify the annihilator of $Y$ with $X/Y$. I assume this is false, since one can simply take some Banach space $Z$ which is not isomorphic to its dual and consider $Y=0$ and $X=Z.$ Am I correct? | |
| Oct 18, 2011 at 20:06 | comment | added | Bill Johnson |
Your question has nothing to do with semi-Fredholm operators. If $Y$ is a closed subspace of Banach space $X$, then the annihilator of $Y$ in $X^{*}$ is canonically isometrically isomorphic to the dual of $X/Y$. Look in any basic text in functional analysis--this will either be in the text or in the problems.
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| Oct 18, 2011 at 19:54 | history | asked | Orbicular | CC BY-SA 3.0 |