Timeline for Closure of the space of Fredholm operators
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 15, 2021 at 19:17 | comment | added | Mikael de la Salle | @YCor Sure, this is what I meant. | |
| Jul 15, 2021 at 11:06 | vote | accept | Overflowian | ||
| Jul 15, 2021 at 10:51 | comment | added | YCor | @MikaeldelaSalle you probably mean Fredholm rather than compact. | |
| Jul 15, 2021 at 10:51 | comment | added | YCor | @WarlockofFiretopMountain see the last few lines in the first page (=page 721) of the linked (1990 Proc AMS) paper. | |
| Jul 15, 2021 at 9:22 | comment | added | Mikael de la Salle | I guess that, by Bouldin's result, the characterization extends to arbitrary Hilbert spaces as follows (using Bouldin's notation): $T$ belongs to the closure of compact operators iff $\textrm{essnull} T$ and $ \textrm{essnull} T^*$ are equal or both finite. | |
| Jul 15, 2021 at 9:22 | comment | added | Overflowian | Thank you, I am convinced by your proof but the assumption does not look straightforward to me. How did you go from Bouldin's theorem, which gives conditions in terms of the spectral projector of $|T|, |T^*|$, to restate it in terms of closedness of the range and dimension of kernel/cokernel? | |
| Jul 15, 2021 at 8:57 | history | edited | YCor | CC BY-SA 4.0 |
fixed typos
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| Jul 15, 2021 at 8:40 | history | answered | YCor | CC BY-SA 4.0 |