Timeline for On a possible attempt to prove the invariant subspace problem
Current License: CC BY-SA 4.0
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| Jun 23, 2020 at 15:02 | comment | added | Manuel Norman | @NikWeaver Nice point! Indeed, my idea was to try to construct a particular rank one operator $K$ which could help to show the existence of a nontrivial invariant subspace, because as you noticed the use of any $K$ would probably be not so useful | |
| Jun 23, 2020 at 14:57 | comment | added | Nik Weaver | That said, even if you don't solve the ISP you might well discover something interesting in this direction ... | |
| Jun 23, 2020 at 14:55 | comment | added | Nik Weaver | Interesting post, but I'm skeptical that this approach will work. The existence of a compact operator with ${\rm rank}(TK - KT) \leq 2$ is trivial, so it's unlikely to be of much help. For instance, fix a unit vector and let $K$ be the orthogonal projection onto its span. Now you give me an arbitrary bounded operator $T$ and I notice that the commutator with my $K$ has rank at most 2. Would that really help me to show that $T$ has a nontrivial invariant subspace? | |
| Jun 23, 2020 at 10:46 | review | First posts | |||
| Jun 23, 2020 at 11:26 | |||||
| Jun 23, 2020 at 10:43 | history | asked | Manuel Norman | CC BY-SA 4.0 |