Timeline for If $\|S\|<\sin\frac{\pi}{2n}$ then $\|P(I-S)^ku\|\neq 0$ for all $k=0,\ldots,n$
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| when toggle format | what | by | license | comment | |
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| Aug 14, 2020 at 3:01 | vote | accept | Andrés Felipe | ||
| Jun 13, 2020 at 17:17 | comment | added | Andrés Felipe | I am reading the article "Geometry of higher order realtive spectrum of linear operator in Hilbert spaces" by Eugene Shargorodsky. In Theorem 5.2 he shows that if $T$ is a bounded operator then $$\left(\sin\left(\frac{π}{2n}\right)\right)^{-1}\|T\|$$ is a bound of the $n$-th order spectrum $\mathrm{Spec}_n(T,\mathcal{L})$ for any closed linear subespace $\mathcal{L}$ of $H$. In his proof, he divides by the quantity $\|Pu_k\|$ but I do not know why this quantity is $\neq 0$. | |
| Feb 23, 2020 at 20:11 | comment | added | Max Horn | What is the motivation for this question? | |
| Feb 23, 2020 at 13:01 | answer | added | Alexandre Eremenko | timeline score: 6 | |
| Feb 23, 2020 at 4:15 | review | Close votes | |||
| Mar 9, 2020 at 17:00 | |||||
| Feb 23, 2020 at 1:25 | review | First posts | |||
| Feb 23, 2020 at 3:55 | |||||
| Feb 23, 2020 at 1:21 | history | asked | Andrés Felipe | CC BY-SA 4.0 |