[Merged by Bors] - feat(Analysis/Normed/Operator): continuous algebra equivalences between continuous endomorphisms are inner

[themathqueen]

This is the continuous version of AlgEquiv.eq_linearEquivConjAlgEquiv. The proof follows the same idea as the non-continuous version.

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[github-actions]

PR summary a36c84ab82

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Topology.Algebra.Module.StrongTopology	1248	1265	+17 (+1.36%)

Import changes for all files

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5 files Mathlib.Analysis.LocallyConvex.PointwiseConvergence Mathlib.Analysis.LocallyConvex.StrongTopology Mathlib.Analysis.Normed.Operator.Compact Mathlib.Topology.Algebra.Module.PointwiseConvergence Mathlib.Topology.Algebra.Module.StrongTopology	17
Mathlib.Analysis.Normed.Operator.ContinuousAlgEquiv (new file)	1763

---

Declarations diff

+ coe_toContinuousLinearMap
+ conjContinuousAlgEquiv
+ conjContinuousAlgEquiv_apply
+ conjContinuousAlgEquiv_apply_apply
+ conjContinuousAlgEquiv_refl
+ conjContinuousAlgEquiv_trans
+ eq_comp_toContinuousLinearMap_symm
+ symm_conjContinuousAlgEquiv
+ symm_conjContinuousAlgEquiv_apply_apply
+ toContinuousLinearMap

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.

---

No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[j-loreaux]

There is a downside to phrasing things in terms of V and W. If they were both V, then you could actually write conjContinuousAlgEquiv as a group homomorphism, and the conclusion of this theorem would be that the range of that homomorphism is ⊤.

I think you should document this somewhere.

[themathqueen]

Yeah, like this Module.End.mulSemiringActionToAlgEquiv_conjAct_surjective.

I was going to leave adding the analogue of that for another PR. But I'll document this on the module docstring for now. I'll add a todo.

[sgouezel]

bors d+
Thanks!

[mathlib-bors]

✌️ themathqueen can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[themathqueen]

bors r+

[mathlib-bors]

Pull request successfully merged into master.

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