Theorems · Theorem · functional analysis
CStarAlgebra.nnnorm_le_iff_of_nonneg
∀ {A : Type u_1} [inst : CStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A] (a : A) (r : NNReal),
autoParam (0 ≤ a) CStarAlgebra.nnnorm_le_iff_of_nonneg._auto_1 → (‖a‖₊ ≤ r ↔ a ≤ (algebraMap NNReal A) r)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 320 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 · cited by 25,697
- RingHomstatement · cited by 10,189
- PartialOrderstatement and proof · cited by 6,410
- Algebra.algebraMapstatement and proof · cited by 4,706
- NNRealstatement and proof · cited by 4,310
- NNNorm.nnnormstatement · cited by 952
- StarOrderedRingstatement and proof · cited by 587
- CStarAlgebrastatement and proof · cited by 123
- NNReal.coe_le_coeproof · cited by 73
- CStarAlgebra.norm_le_iff_le_algebraMapproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- CStarAlgebra.nnnorm_le_natCast_iff_of_nonnegproof · cited by 0