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[Merged by Bors] - feat(analysis/complex/liouville): prove Liouville's theorem #12095

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[Merged by Bors] - feat(analysis/complex/liouville): prove Liouville's theorem #12095

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@urkud urkud commented Feb 17, 2022 •
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This statement is already useful but we should generalize later.

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@urkud urkud added awaiting-review The author would like community review of the PR awaiting-CI The author would like to see what CI has to say before doing more work. labels Feb 17, 2022
@github-actions github-actions bot removed the awaiting-CI The author would like to see what CI has to say before doing more work. label Feb 17, 2022
@j-loreaux j-loreaux mentioned this pull request Feb 18, 2022
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I think this looks good, aside from the naming comments below. It is certainly enough for basic applications of Liouville's theorem. I have already used it for showing the spectrum is nonempty.

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@sgouezel sgouezel added awaiting-author A reviewer has asked the author a question or requested changes and removed awaiting-review The author would like community review of the PR labels Feb 21, 2022
@urkud urkud added awaiting-review The author would like community review of the PR and removed awaiting-author A reviewer has asked the author a question or requested changes labels Feb 27, 2022
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bors r+
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bors bot pushed a commit that referenced this pull request Feb 27, 2022
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feat(analysis/complex/liouville): prove Liouville's theorem (#12095)
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@github-actions github-actions bot added ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.) and removed awaiting-review The author would like community review of the PR labels Feb 27, 2022
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Pull request successfully merged into master.

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@bors bors bot changed the title feat(analysis/complex/liouville): prove Liouville's theorem [Merged by Bors] - feat(analysis/complex/liouville): prove Liouville's theorem Feb 27, 2022
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@bors bors bot deleted the YK-liouville branch February 27, 2022 21:56
bors bot pushed a commit that referenced this pull request Mar 1, 2022
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feat(algebra/algebra/spectrum, analysis/normed_space/spectrum): prove…
b45657f 
… the spectrum of any element in a complex Banach algebra is nonempty (#12115)

This establishes that the spectrum of any element in a (nontrivial) complex Banach algebra is nonempty. The nontrivial assumption is necessary, as otherwise the only element is invertible. In addition, we establish some properties of the resolvent function; in particular, it tends to zero at infinity.

- [x] depends on: #12095 



Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
@alreadydone alreadydone mentioned this pull request Nov 4, 2022
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