Timeline for Kernels of derivations and hyperreflexivity
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Sep 6 at 16:55 | comment | added | E. Papapetros | Exactly, it is still open. Also, the very large class of those $II_{\infty}$ commutants with $II_1$ commutants, which are hyperreflexive, automatically gives us a very large class of $II_1$ factors satisfying Kadison's similarity problem. | |
| Sep 6 at 16:46 | comment | added | David Gao | Hmm, that would be more challenging. There are plenty of II$_1$ factors that can be generated by finitely many projections, but whether this holds for all II$_1$ factors should still be open, if I’m not mistaken. But this should still mean your conjecture implies a very large class of II$_\infty$ factors with II$_1$ commutants are hyperreflexive, which makes this quite hard. | |
| Sep 6 at 16:41 | comment | added | E. Papapetros | Dear @DavidGao, it is known by Lemma 1.3 on a paper of J. Kraus and David Larson entitle "Reflexivity and distance formulae". Also, any $II_1$ factor $M$ with $II_{\infty}$ commutant $M^\prime$ is hyperreflexive. The open case is if $M^\prime$ is hyperreflexive. | |
| Sep 6 at 14:09 | history | edited | Michael Hardy | CC BY-SA 4.0 |
added 3 characters in body
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| Sep 6 at 12:31 | comment | added | David Gao | Also, if I’m not mistaken, any type II$_\infty$ factor can be generated by finitely many projections. $B(H)$ is hyperreflexive, so your claim would imply any II$_1$ factor with II$_\infty$ commutant is hyperreflexive, which, if I’m not mistaken, is still open according to your comments on one of your previous questions. | |
| Sep 6 at 12:15 | comment | added | David Gao | What exactly is the known result regarding $\text{ker}(\pi)$ that you referred to? Any central compression of a hyperreflexive vNa is hyperreflexive? (Also, everything here is a vNa, you can define hyperreflexivity for just vNa’s instead of for general operator spaces.) | |
| S Sep 6 at 9:45 | review | First questions | |||
| Sep 6 at 9:50 | |||||
| S Sep 6 at 9:45 | history | asked | E. Papapetros | CC BY-SA 4.0 |