Theorems · Definition · functional analysis
PositiveLinearMap.gnsStarAlgHom
{A : Type u_2} →
[inst : CStarAlgebra A] →
[inst_1 : PartialOrder A] → [inst_2 : StarOrderedRing A] → (f : A →ₚ[ℂ] ℂ) → A →⋆ₐ[ℂ] f.GNS →L[ℂ] f.GNSThe 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 unital C⋆-algebra.
This is the unital version of gnsNonUnitalStarAlgHom.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 327 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement and proof · cited by 18,349
- PartialOrderstatement and proof · cited by 6,410
- Complexstatement and proof · cited by 5,565
- ContinuousLinearMapstatement and proof · cited by 5,352
- StarOrderedRingstatement and proof · cited by 587
- StarAlgHomstatement · cited by 215
- NonUnitalStarAlgHomproof · cited by 208
- CStarAlgebrastatement and proof · cited by 123
- Complex.partialOrderstatement · cited by 64
- PositiveLinearMapstatement and proof · cited by 52
- MulActionHom.toFunproof · cited by 46
- DistribMulActionHom.toMulActionHomproof · cited by 30
Cited by1
Results whose statement or proof uses this declaration.
- PositiveLinearMap.gnsStarAlgHom_applystatement and proof · cited by 0