Theorems · Theorem · functional analysis
Unitary.expUnitary_eq_mul_inv
∀ {A : Type u_1} [inst : CStarAlgebra A] (u v : ↥(unitary A)),
‖↑u - ↑v‖ < 2 → selfAdjoint.expUnitary (Unitary.argSelfAdjoint (u * star v)) = u * star v- Cited by
- 1 results in Mathlib
- Foundations
- Depth 316 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- Submonoidstatement · cited by 3,086
- Star.starstatement · cited by 1,082
- unitarystatement and proof · cited by 207
- CStarAlgebrastatement and proof · cited by 123
- selfAdjoint.expUnitarystatement · cited by 19
- Unitary.argSelfAdjointstatement · cited by 13
- expUnitary_argSelfAdjointproof · cited by 2
- Unitary.norm_sub_eqproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Unitary.mem_pathComponentOne_iffproof · cited by 0