Theorems · Definition · functional analysis
Unitary.path
{A : Type u_1} → [inst : CStarAlgebra A] → (u v : ↥(unitary A)) → ‖↑v - ↑u‖ < 2 → Path u vThe path t ↦ expUnitary (t • argSelfAdjoint (v * star u)) * u
from u : unitary A to v when ‖v - u‖ < 2.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 318 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Set.Elemproof · cited by 7,166
- Norm.normstatement and proof · cited by 5,413
- Submonoidstatement · cited by 3,086
- Star.starproof · cited by 1,082
- unitIntervalproof · cited by 607
- Pathstatement · cited by 318
- unitarystatement and proof · cited by 207
- CStarAlgebrastatement and proof · cited by 123
- selfAdjoint.expUnitaryproof · cited by 19
- Unitary.argSelfAdjointproof · cited by 13
Cited by4
Results whose statement or proof uses this declaration.
- Unitary.path_applystatement and proof · cited by 1
- Unitary.joinedproof · cited by 0
- Unitary.isPathConnected_ballproof · cited by 0
- Unitary.path.congr_simpstatement and proof · cited by 0