Timeline for Linearization stability condition
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Sep 18 at 7:17 | history | undeleted | Gordhob Brain | ||
| Sep 17 at 21:19 | history | deleted | Gordhob Brain | via Vote | |
| Nov 21, 2022 at 8:01 | comment | added | Jochen Wengenroth | Instead of surjective with splitting kernel you can also say that $T\phi(x_0)$ has a continuous linear right inverse. | |
| Nov 20, 2022 at 22:39 | history | edited | Gordhob Brain | CC BY-SA 4.0 |
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| Nov 20, 2022 at 20:15 | comment | added | Gordhob Brain | Thanks so much. | |
| Nov 20, 2022 at 16:52 | comment | added | Igor Khavkine | The sentence you highlighted in bold is completely analogous to the finite dimensional implicit function theorem, I don't see what is there to explain. The terminology "splitting kernel" I guess is not the only way to phrase it. I believe it is simply a necessary hypothesis to apply the Banach space version of the implicit function theorem, that $X = T_{x_0}X \cong \ker T\Phi(x_0) \times Z$, where $Z\subset T_{x_0}X$ complements $\ker T\Phi(x_0)$. In general Banach spaces, not all subspaces are complemented. | |
| Nov 20, 2022 at 10:32 | history | edited | YCor | CC BY-SA 4.0 |
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| Nov 20, 2022 at 1:21 | history | edited | Gordhob Brain | CC BY-SA 4.0 |
edited tags; edited title
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| Nov 20, 2022 at 1:11 | history | edited | Gordhob Brain | CC BY-SA 4.0 |
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| Nov 20, 2022 at 0:55 | history | asked | Gordhob Brain | CC BY-SA 4.0 |