Theorems · Definition · functional analysis
PositiveLinearMap.gnsNonUnitalStarAlgHom
{A : Type u_1} →
[inst : NonUnitalCStarAlgebra A] →
[inst_1 : PartialOrder A] → (f : A →ₚ[ℂ] ℂ) → [inst_2 : StarOrderedRing A] → A →⋆ₙₐ[ℂ] f.GNS →L[ℂ] f.GNSThe non-unital ⋆-homomorphism/⋆-representation of A into the algebra of bounded operators on
a Hilbert space that is constructed from a positive linear functional f on a possibly non-unital
C⋆-algebra.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 324 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- StarOrderedRingstatement and proof · cited by 587
- NonUnitalStarAlgHomstatement · cited by 208
- NonUnitalCStarAlgebrastatement and proof · cited by 149
- Complex.partialOrderstatement · cited by 64
- PositiveLinearMapstatement and proof · cited by 52
- PositiveLinearMap.PreGNSstatement · cited by 10
- PositiveLinearMap.leftMulMapPreGNSproof · cited by 4
- ContinuousLinearMap.completionproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- PositiveLinearMap.gnsStarAlgHomproof · cited by 1
- PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coestatement · cited by 0
- PositiveLinearMap.gnsStarAlgHom_applystatement · cited by 0
- PositiveLinearMap.gnsNonUnitalStarAlgHom_applystatement · cited by 0