feat(Analysis/Operator/Normed/Extend): add LinearIsometry.extendOfIsometry

[TJHeeringa]

Adds LinearIsometry.extendOfIsometry, the extention of a linear isometry f : E ≃ₗᵢ[𝕜] F between normed spaces to a linear isometry Eₗ →ₗᵢ[𝕜] Fₗ between Banach spaces with a dense map e₁ : E →ₗ[𝕜] Eₗ, a linear map e₂ : F →ₗ[𝕜] Fₗ and the corresponding norm estimates.

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LinearEquiv and ContinuousLinearMap have this extension, but LinearIsometry does not.

I called this extendOfIsometry because LinearIsometry.extend map already exists and LinearEquiv has a similar map. That map is the special case of LinearIsometry.extendOfIsometry when the input space is a submodule of a finite dimensional inner product space. A case could be made for calling LinearIsometry.extendOfIsometry LinearIsometry.extend and renaming the existing LinearIsometry.extendOfIsometry to LinearIsometry.extendOfFin.

[github-actions]

PR summary b566cce7b1

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ extendOfIsometry
+ extendOfIsometry_apply
+ extendOfIsometry_eq

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit b566cce).

• +3 new declarations
• −0 removed declarations

+LinearIsometry.extendOfIsometry
+LinearIsometry.extendOfIsometry_apply
+LinearIsometry.extendOfIsometry_eq

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit b566cce7b1
Reference commit 375d54da29

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/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).