Theorems · Theorem · functional analysis
PositiveLinearMap.preGNS_inner_def
∀ {A : Type u_1} [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] (f : A →ₚ[ℂ] ℂ) [inst_2 : StarOrderedRing A]
(a b : f.PreGNS), inner ℂ a b = f (star (f.ofPreGNS a) * f.ofPreGNS b)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 318 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- PartialOrderstatement and proof · cited by 6,410
- Complexstatement and proof · cited by 5,565
- LinearEquivstatement · cited by 3,317
- Inner.innerstatement · cited by 1,089
- Star.starstatement · 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
- PositiveLinearMap.PreGNSstatement and proof · cited by 10
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