Theorems · Theorem · functional analysis
PositiveLinearMap.leftMulMapPreGNS_apply
∀ {A : Type u_1} [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] (f : A →ₚ[ℂ] ℂ) [inst_2 : StarOrderedRing A]
(a : A) (x : f.PreGNS), (f.leftMulMapPreGNS a) x = f.toPreGNS (a * f.ofPreGNS x)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 321 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- RingHom.idstatement · cited by 18,349
- PartialOrderstatement and proof · cited by 6,410
- Complexstatement and proof · cited by 5,565
- ContinuousLinearMapstatement · cited by 5,352
- LinearEquivstatement · cited by 3,317
- StarOrderedRingstatement and proof · cited by 587
- NonUnitalCStarAlgebrastatement and proof · cited by 149
- Complex.partialOrderstatement · cited by 64
- PositiveLinearMapstatement and proof · cited by 52
- PositiveLinearMap.PreGNSstatement and proof · cited by 10
- PositiveLinearMap.ofPreGNSstatement · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coeproof · cited by 0
- PositiveLinearMap.leftMulMapPreGNS_mul_eq_compproof · cited by 0