Timeline for Is this consequence of the invariant subspace problem known?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Feb 8, 2019 at 5:03 | vote | accept | Nik Weaver | ||
| Feb 8, 2019 at 5:02 | comment | added | Nik Weaver | Okay, that makes sense now. I think it would be better to say "inherited by quotient and restrictions" because you're first restricting to $M$ and then quotienting by $N$. Not a criticism of you, Matt, I realize you didn't create the terminology. | |
| Feb 8, 2019 at 4:43 | comment | added | Matt Kennedy | Thanks Yemon! You are correct, and I have clarified my answer. | |
| S Feb 8, 2019 at 4:42 | history | edited | Matt Kennedy | CC BY-SA 4.0 |
added definition for "inherited by quotients"
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| S Feb 8, 2019 at 4:42 | history | suggested | Amir Sagiv | CC BY-SA 4.0 |
very minor tex edits
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| Feb 8, 2019 at 4:27 | comment | added | Yemon Choi | @NikWeaver I'm far from fluent in the language here, but I think "quotient" refers to a single operator and not to an algebra of operators, and it means something like: if $T$ is your operator and it has invariant subspaces $V\subset W$ then the "quotient" operator is the one induced on $W/V$. (But Matt should correct me if I have misremembered or misunderstood) | |
| Feb 8, 2019 at 3:52 | comment | added | Nik Weaver | Does it mean "quotient by an invariant subspace"? Then the result seems false. For instance, say P is the property "is isomorphic to $M_1$ or to the subalgebra of $M_3$ consisting of all matrices of the form $\left[\begin{matrix}*&*&*\cr *&*&*\cr 0&0&*\end{matrix}\right]$". The only invariant subspace of the latter algebra is $\mathbb{C}^2 \oplus 0$, the quotient by which leaves $M_1$. So this property is inherited by quotients (in the only sense I can think of), but the algebra isn't triangularizable. Or does "property" mean something different? | |
| Feb 8, 2019 at 3:26 | comment | added | Nik Weaver | What is meant by a "quotient" in this context? | |
| Feb 8, 2019 at 3:24 | review | Suggested edits | |||
| S Feb 8, 2019 at 4:42 | |||||
| Feb 8, 2019 at 3:10 | comment | added | Yemon Choi | Welcome to the time-sink, I mean hellmouth, I mean, erm, best use of one's time when not doing admin | |
| Feb 8, 2019 at 2:45 | review | First posts | |||
| Feb 8, 2019 at 3:25 | |||||
| Feb 8, 2019 at 2:42 | history | answered | Matt Kennedy | CC BY-SA 4.0 |