Theorems · Theorem · functional analysis
PositiveLinearMap.preGNS_norm_sq
∀ {A : Type u_1} [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] (f : A →ₚ[ℂ] ℂ) [inst_2 : StarOrderedRing A]
(a : f.PreGNS), ↑‖a‖ ^ 2 = f (star (f.ofPreGNS a) * f.ofPreGNS a)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 317 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites21
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
- Norm.normstatement · cited by 5,413
- LinearEquivstatement · cited by 3,317
- Complex.ofRealstatement and proof · cited by 1,654
- Star.starstatement and proof · cited by 1,082
- Complex.reproof · cited by 882
- StarOrderedRingstatement and proof · cited by 587
- Real.sqrtproof · cited by 545
- NonUnitalCStarAlgebrastatement and proof · cited by 149
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