[Merged by Bors] - feat: The norm on Unitization is a C⋆-norm
#5393
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Would it be a lot of trouble to split this into a PR that just renames files, and the other one with the actual changes made here? |
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RegularNormedAlgebra and add the C⋆-norm on the UnitizationUnitization is a C⋆-norm
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@dupuisf I have split this into more manageable chunks. 5741 is easy and just renames instances, 5743 is easy and just renames the file, 5742 is the bulk of the work ( |
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…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
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…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
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…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
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Co-authored-by: Frédéric Dupuis <31101893+dupuisf@users.noreply.github.com>
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Unitization is a C⋆-normUnitization is a C⋆-norm
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This shows that C⋆-algebras are always
RegularNormedAlgebras, so that theirUnitizationis equipped with a norm. Moreover, we show this norm is a C⋆-norm.PseudoMetricSpace.replaceUniformity#5330Unitization#5741RegularNormedAlgebraand add the norm on theUnitization#5742