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[Merged by Bors] - chore: rename instances related to Unitization #5741

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Okay, maybe not quite < 20 s of review time, but it's close.

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@j-loreaux j-loreaux added awaiting-review The author would like community review of the PR easy < 20s of review time. See the lifecycle page for guidelines. labels Jul 6, 2023
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bors merge

@github-actions github-actions bot added ready-to-merge This PR has been sent to bors. and removed awaiting-review The author would like community review of the PR labels Jul 7, 2023
bors bot pushed a commit that referenced this pull request Jul 7, 2023
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@bors bors bot changed the title chore: rename instances related to Unitization [Merged by Bors] - chore: rename instances related to Unitization Jul 7, 2023
@bors bors bot closed this Jul 7, 2023
@bors bors bot deleted the j-loreaux/Unitization-instance-names branch July 7, 2023 03:54
qawbecrdtey pushed a commit to qawbecrdtey/greedoid-mathlib4 that referenced this pull request Jul 7, 2023
bors bot pushed a commit that referenced this pull request Aug 17, 2023
…ion` (#5742)

This constructs a norm on the `Unitization 𝕜 A` of a (possibly non-unital) normed algebra `A`, subject to the condition that `ContinuousLinearMap.mul 𝕜 A` is an isometry. A norm on `A` satisfying this property is said to be regular so we add the class `RegularNormedAlgebra` where this construction makes sense.

This norm is particularly nice because, among norms on the unitization of a `RegularNormedAlgebra`, this norm is minimal. Moreover, it is the (necessarily unique) C⋆-norm on the unitization when the norm on `A` is a C⋆-norm (see #5393)

- [x] depends on: #5741
bors bot pushed a commit that referenced this pull request Aug 17, 2023
…ion` (#5742)

This constructs a norm on the `Unitization 𝕜 A` of a (possibly non-unital) normed algebra `A`, subject to the condition that `ContinuousLinearMap.mul 𝕜 A` is an isometry. A norm on `A` satisfying this property is said to be regular so we add the class `RegularNormedAlgebra` where this construction makes sense.

This norm is particularly nice because, among norms on the unitization of a `RegularNormedAlgebra`, this norm is minimal. Moreover, it is the (necessarily unique) C⋆-norm on the unitization when the norm on `A` is a C⋆-norm (see #5393)

- [x] depends on: #5741
bors bot pushed a commit that referenced this pull request Aug 18, 2023
…ion` (#5742)

This constructs a norm on the `Unitization 𝕜 A` of a (possibly non-unital) normed algebra `A`, subject to the condition that `ContinuousLinearMap.mul 𝕜 A` is an isometry. A norm on `A` satisfying this property is said to be regular so we add the class `RegularNormedAlgebra` where this construction makes sense.

This norm is particularly nice because, among norms on the unitization of a `RegularNormedAlgebra`, this norm is minimal. Moreover, it is the (necessarily unique) C⋆-norm on the unitization when the norm on `A` is a C⋆-norm (see #5393)

- [x] depends on: #5741
bors bot pushed a commit that referenced this pull request Aug 22, 2023
This shows that C⋆-algebras are always `RegularNormedAlgebra`s, so that their `Unitization` is equipped with a norm. Moreover, we show this norm is a C⋆-norm.

- [x] depends on: #5330
- [x] depends on: #5741
- [x] depends on: #5742 
- [x] depends on: #5743
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