Theorems · Theorem · ring theory
IsSelfAdjoint.map
∀ {F : Type u_3} {R : Type u_4} {S : Type u_5} [inst : Star R] [inst_1 : Star S] [inst_2 : FunLike F R S]
[StarHomClass F R S] {x : R}, IsSelfAdjoint x → ∀ (f : F), IsSelfAdjoint (f x)Functions in a StarHomClass preserve self-adjoint elements.
- Defined in
- Mathlib.Algebra.Star.SelfAdjoint
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- StarStarFunLikeStarHomClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- FunLikestatement and proof · cited by 2,560
- Star.starproof · cited by 1,082
- IsSelfAdjointstatement and proof · cited by 545
- Starstatement and proof · cited by 496
- StarHomClassstatement and proof · cited by 76
- StarHomClass.map_starproof · cited by 20
Cited by7
Results whose statement or proof uses this declaration.
- ProbabilityTheory.covarianceBilin_multivariateGaussianproof · cited by 3
- NonUnitalStarAlgHom.nnnorm_apply_leproof · cited by 2
- NonUnitalStarAlgHom.norm_mapproof · cited by 2
- IsSelfAdjoint.map_spectrum_realproof · cited by 1
- StarSubalgebra.coe_isUnitproof · cited by 1
- isSelfAdjoint_mapproof · cited by 0
- IsStarProjection.mapproof · cited by 0