Theorems · Theorem · functional analysis
PositiveLinearMap.apply_le_of_isSelfAdjoint
∀ {B₁ : Type u_3} {B₂ : Type u_4} [inst : CStarAlgebra B₁] [inst_1 : CStarAlgebra B₂] [inst_2 : PartialOrder B₁]
[inst_3 : PartialOrder B₂] [StarOrderedRing B₁] (f : B₁ →ₚ[ℂ] B₂) (x : B₁),
IsSelfAdjoint x → f x ≤ f ((algebraMap ℝ B₁) ‖x‖)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 312 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 and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHomstatement · cited by 10,189
- PartialOrderstatement and proof · cited by 6,410
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- Algebra.algebraMapstatement and proof · cited by 4,706
- StarOrderedRingstatement and proof · cited by 587
- IsSelfAdjointstatement and proof · cited by 545
- CStarAlgebrastatement and proof · cited by 123
- PositiveLinearMapstatement and proof · cited by 52
- OrderHomClass.monoproof · cited by 22
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