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feat: bounded linear functional is monotone iff ‖f‖ = f 1 - #86

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feat: bounded linear functional is monotone iff ‖f‖ = f 1#86
themathqueen wants to merge 16 commits into
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CLM_monotone_iff

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@themathqueen themathqueen commented Jun 30, 2026

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Comment thread LeanOA/CStarAlgebra/PositiveLinearFunctional.lean Outdated
Comment thread LeanOA/CStarAlgebra/PositiveLinearFunctional.lean Outdated
by_cases ‖f‖ = 0
· simp_all
suffices ∀ (t : ℝ), ‖f a + Complex.I * t * ‖f‖‖ ^ 2 ≤ ‖f‖ ^ 2 * (‖a‖ ^ 2 + t ^ 2) by
contrapose! this; conv_rhs => simp [Complex.normSq, ← Complex.normSq_eq_norm_sq]

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I think this is a bug in the flexible linter 👀
shouldn't this not be allowed?

Comment thread LeanOA/CStarAlgebra/PositiveLinearFunctional.lean Outdated
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