Theorems · Definition · functional analysis
PositiveLinearMap.preGNSpreInnerProdSpace
{A : Type u_1} →
[inst : NonUnitalCStarAlgebra A] →
[inst_1 : PartialOrder A] → (f : A →ₚ[ℂ] ℂ) → [StarOrderedRing A] → PreInnerProductSpace.Core ℂ f.PreGNSThe (semi-)inner product space whose elements are the elements of A, but which has an
inner product-induced norm that is different from the norm on A and which is induced by f.
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- Foundations
- Depth 315 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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- DFunLike.coeproof · cited by 62,936
- PartialOrderstatement and proof · cited by 6,410
- Complexstatement and proof · cited by 5,565
- Star.starproof · cited by 1,082
- StarOrderedRingstatement and proof · cited by 587
- NonUnitalCStarAlgebrastatement and proof · cited by 149
- Complex.partialOrderstatement · cited by 64
- PositiveLinearMapstatement and proof · cited by 52
- PreInnerProductSpace.Corestatement · cited by 46
- PositiveLinearMap.PreGNSstatement and proof · cited by 10
- PositiveLinearMap.ofPreGNSproof · cited by 8
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