Theorems · Theorem · functional analysis
PositiveLinearMap.norm_apply_le_of_nonneg
∀ {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] [StarOrderedRing B₂] (f : B₁ →ₚ[ℂ] B₂) (x : B₁),
0 ≤ x → ‖f x‖ ≤ ‖f 1‖ * ‖x‖- Cited by
- 0 results in Mathlib
- Foundations
- Depth 321 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites20
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
- PartialOrderstatement and proof · cited by 6,410
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- mul_commproof · cited by 2,262
- Complex.ofRealproof · cited by 1,654
- StarOrderedRingstatement and proof · cited by 587
- norm_smulproof · cited by 242
- CStarAlgebrastatement and proof · cited by 123
- Algebra.algebraMap_eq_smul_oneproof · cited by 119
- norm_normproof · cited by 113
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