Theorems · Definition · functional analysis
selfAdjoint.expUnitaryPathToOne
{A : Type u_1} → [inst : CStarAlgebra A] → (x : ↥(selfAdjoint A)) → Path 1 (selfAdjoint.expUnitary x)For a selfadjoint element x in a C⋆-algebra, this is the path from 1 to expUnitary x
given by t ↦ expUnitary (t • x).
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 184 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.Elemproof · cited by 7,166
- AddSubgroupstatement · cited by 3,232
- Submonoidstatement · cited by 3,086
- unitIntervalproof · cited by 607
- Pathstatement · cited by 318
- unitarystatement · cited by 207
- selfAdjointstatement and proof · cited by 135
- CStarAlgebrastatement and proof · cited by 123
- selfAdjoint.expUnitarystatement and proof · cited by 19
Cited by2
Results whose statement or proof uses this declaration.
- selfAdjoint.joined_one_expUnitaryproof · cited by 1
- selfAdjoint.expUnitaryPathToOne_applystatement and proof · cited by 0