Timeline for Taylor spectrum of commuting operators
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Dec 5, 2018 at 13:05 | history | edited | Igor Khavkine | CC BY-SA 4.0 |
Fixed typos.
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| Dec 5, 2018 at 13:00 | vote | accept | Student | ||
| Dec 5, 2018 at 10:25 | comment | added | Igor Khavkine | @Student I have added some explanation about the use of a contracting homotopy to show that a complex is exact. This is actually a more general version of the same argument as the one given in the last paragraph of your quote from Taylor (there, $b$ is the homotopy map). As to the spectral inclusion question, I suspect yes, but I have worked out only the case for $d=2$ (basically, my answer above). | |
| Dec 5, 2018 at 10:21 | history | edited | Igor Khavkine | CC BY-SA 4.0 |
added 1525 characters in body
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| Dec 4, 2018 at 8:00 | comment | added | Student | Let $\mathbf{T}=(T_1,\cdots,T_d)\in \mathcal{B}(\mathcal{H})^d$ be a $d$-tuple of commuting operators. It is true that $$\sigma_T(\mathbf{T})\subset \sigma(T_1)\times \cdots \times\sigma(T_d)\;?$$ If the answer a true I find another idea. Thanks a lot for your help. | |
| Dec 4, 2018 at 5:46 | comment | added | Student | Dear Professor, While the three identities are obviously true, I do not know enough about the Koszul complex to see the connection. I also don't know about the connection between the eigenvalues of I and A and the Koszul complex. I hope that you explain me a bit or to propose me a good reference. Thanks a lot. | |
| Nov 30, 2018 at 11:24 | comment | added | Igor Khavkine | @Student, ah yes, a couple of typos. Thanks for noticing. Now fixed! | |
| Nov 30, 2018 at 11:23 | history | edited | Igor Khavkine | CC BY-SA 4.0 |
edited body
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| Nov 30, 2018 at 10:38 | comment | added | Student | Ok thank you. I think there is a small mistake. You use $\Lambda$ but you mean $\lambda$ | |
| Nov 30, 2018 at 10:37 | comment | added | Igor Khavkine | @Student, these are all block matrices. Multiply everything explicitly to check the identities explicitly. As an exercise, to check your understanding, reproduce the same identities by using $R_A(\mu)$. | |
| Nov 30, 2018 at 10:29 | comment | added | Student | Thank you for your answer but please I don't understand how you get the three idenity and what you mean by $[ ]$? | |
| Nov 30, 2018 at 10:15 | history | answered | Igor Khavkine | CC BY-SA 4.0 |