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[Merged by Bors] - feat: any element satisfying the predicate of a continuous functional calculus has nonempty spectrum#16343

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[Merged by Bors] - feat: any element satisfying the predicate of a continuous functional calculus has nonempty spectrum#16343
j-loreaux wants to merge 4 commits intomasterfrom
j-loreaux/CFC.spectrum_nonempty

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@j-loreaux j-loreaux commented Aug 31, 2024

In particular, this gives us that the ℝ-spectrum of selfadjoint elements and the ℝ≥0-spectrum of nonnegative elements in a C⋆-algebra are nonempty.

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@j-loreaux j-loreaux added the t-analysis Analysis (normed *, calculus) label Aug 31, 2024
@j-loreaux j-loreaux requested a review from dupuisf August 31, 2024 01:04
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github-actions bot commented Aug 31, 2024 •
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PR summary 8122eb80bc

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ CFC.spectrum_nonempty
+ IsSelfAdjoint.spectrum_nonempty
+ NNReal.spectrum_nonempty

You can run this locally as follows 
## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

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dupuisf commented Aug 31, 2024

Looks good!

bors r+

@github-actions github-actions bot added the ready-to-merge This PR has been sent to bors. label Aug 31, 2024
@j-loreaux j-loreaux mentioned this pull request Aug 31, 2024
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mathlib-bors bot pushed a commit that referenced this pull request Aug 31, 2024
@j-loreaux
feat: any element satisfying the predicate of a continuous functional…
16a2ce5 
… calculus has nonempty spectrum (#16343)

In particular, this gives us that the `ℝ`-spectrum of selfadjoint elements and the `ℝ≥0`-spectrum of nonnegative elements in a C⋆-algebra are nonempty.
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mathlib-bors bot commented Aug 31, 2024

This PR was included in a batch that was canceled, it will be automatically retried

mathlib-bors bot pushed a commit that referenced this pull request Aug 31, 2024
@j-loreaux
feat: any element satisfying the predicate of a continuous functional…
dbb26bf 
… calculus has nonempty spectrum (#16343)

In particular, this gives us that the `ℝ`-spectrum of selfadjoint elements and the `ℝ≥0`-spectrum of nonnegative elements in a C⋆-algebra are nonempty.
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mathlib-bors bot commented Aug 31, 2024

Pull request successfully merged into master.

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@mathlib-bors mathlib-bors bot changed the title feat: any element satisfying the predicate of a continuous functional calculus has nonempty spectrum [Merged by Bors] - feat: any element satisfying the predicate of a continuous functional calculus has nonempty spectrum Aug 31, 2024
@mathlib-bors mathlib-bors bot closed this Aug 31, 2024
@mathlib-bors mathlib-bors bot deleted the j-loreaux/CFC.spectrum_nonempty branch August 31, 2024 14:49
bjoernkjoshanssen pushed a commit that referenced this pull request Sep 9, 2024
@j-loreaux @bjoernkjoshanssen
feat: any element satisfying the predicate of a continuous functional…
42e2be6 
… calculus has nonempty spectrum (#16343)

In particular, this gives us that the `ℝ`-spectrum of selfadjoint elements and the `ℝ≥0`-spectrum of nonnegative elements in a C⋆-algebra are nonempty.
bjoernkjoshanssen pushed a commit that referenced this pull request Sep 9, 2024
@j-loreaux @bjoernkjoshanssen
feat: any element satisfying the predicate of a continuous functional…
3bd76dd 
… calculus has nonempty spectrum (#16343)

In particular, this gives us that the `ℝ`-spectrum of selfadjoint elements and the `ℝ≥0`-spectrum of nonnegative elements in a C⋆-algebra are nonempty.
bjoernkjoshanssen pushed a commit that referenced this pull request Sep 12, 2024
@j-loreaux @bjoernkjoshanssen
feat: any element satisfying the predicate of a continuous functional…
6366c88 
… calculus has nonempty spectrum (#16343)

In particular, this gives us that the `ℝ`-spectrum of selfadjoint elements and the `ℝ≥0`-spectrum of nonnegative elements in a C⋆-algebra are nonempty.
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