Theorems · Theorem · functional analysis
expUnitary_argSelfAdjoint
∀ {A : Type u_1} [inst : CStarAlgebra A] {u : ↥(unitary A)},
‖↑u - 1‖ < 2 → selfAdjoint.expUnitary (Unitary.argSelfAdjoint u) = u- Cited by
- 2 results in Mathlib
- Foundations
- Depth 315 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CStarAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites49
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Set.imageproof · cited by 5,609
- Complexproof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- Submonoidstatement · cited by 3,086
- one_mulproof · cited by 2,841
- zero_addproof · cited by 2,366
- MulZeroClass.mul_zeroproof · cited by 2,091
- Complex.ofRealproof · cited by 1,654
- MulZeroClass.zero_mulproof · cited by 1,625
- ContinuousOnproof · cited by 1,411
- sub_selfproof · cited by 996
Cited by2
Results whose statement or proof uses this declaration.
- Unitary.two_mul_one_sub_cos_norm_argSelfAdjointproof · cited by 2
- Unitary.expUnitary_eq_mul_invproof · cited by 1