Theorems · Theorem · functional analysis
Unitary.norm_argSelfAdjoint
∀ {A : Type u_1} [inst : CStarAlgebra A] {u : ↥(unitary A)},
‖↑u - 1‖ < 2 → ‖Unitary.argSelfAdjoint u‖ = Real.arccos (1 - ‖↑u - 1‖ ^ 2 / 2)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 317 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CStarAlgebra
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Norm.normstatement and proof · cited by 5,413
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- unitarystatement and proof · cited by 207
- neg_eq_zeroproof · cited by 171
- sub_eq_zero_of_eqproof · cited by 154
- selfAdjointstatement · cited by 135
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