feat: the limit of the norm of the evaluation of f at any increasing approximate unit is the norm of f#77
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themathqueen merged 17 commits intomasterfrom Mar 23, 2026
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themathqueen
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Mar 22, 2026
| refine CStarAlgebra.norm_le_norm_of_nonneg_of_le (f.map_nonneg (star_mul_self_nonneg _)) ?_ | ||
| exact f.mono <| hx1.star_eq.symm ▸ CStarAlgebra.mul_self_le_of_nonneg_of_norm_le_one hx1 hx2 | ||
| conv_lhs => rw [← hx1.star_eq] | ||
| grw [cauchy_schwarz_star_mul f x a, mul_pow, Real.sq_sqrt (norm_nonneg _), |
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Note: cauchy_schwarz_foo is probably not a great name? Could be an abbreviation though for discoverability?
themathqueen
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Mar 22, 2026
| have h2 : ∀ᶠ x in l, ‖(f : A →L[ℂ] ℂ)‖ - ε / 2 < ‖f x‖ := by | ||
| obtain ⟨_, ⟨a, ha1, rfl⟩, ha2⟩ := exists_lt_of_lt_csSup (b := ‖(f : A →L[ℂ] ℂ)‖ - ε / 4) | ||
| ((Metric.nonempty_closedBall (x := 0).mpr zero_le_one).image (‖f ·‖)) | ||
| (by grind [f.toContinuousLinearMap.sSup_unitClosedBall_eq_norm]) |
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Important note: in Mathlib, unitClosedBall is used. So we should change all forms of closedUnitBall in LeanOA to that.
I think closedBall 0 1 should be an abbreviation since it's used a lot, it would at least allow for consistent naming.
j-loreaux
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Mar 22, 2026
LeanOA/Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Order.lean
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| theorem tendsto_isIncreasingApproximateUnit_nhds_opNorm {A : Type*} [NonUnitalCStarAlgebra A] | ||
| [PartialOrder A] [StarOrderedRing A] (f : A →ₚ[ℂ] ℂ) {l : Filter A} | ||
| (hl : l.IsIncreasingApproximateUnit) : l.Tendsto (‖f ·‖) (𝓝 ‖(f : A →L[ℂ] ℂ)‖) := by |
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