Theorems · Theorem · functional analysis
CStarAlgebra.norm_le_one_iff_of_nonneg
∀ {A : Type u_1} [inst : CStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A] (a : A),
autoParam (0 ≤ a) CStarAlgebra.norm_le_one_iff_of_nonneg._auto_1 → (‖a‖ ≤ 1 ↔ a ≤ 1)- Cited by
- 6 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- PartialOrderstatement and proof · cited by 6,410
- Norm.normstatement and proof · cited by 5,413
- Algebra.algebraMapproof · cited by 4,706
- map_oneproof · cited by 861
- StarOrderedRingstatement and proof · cited by 587
- zero_le_oneproof · cited by 316
- CStarAlgebrastatement and proof · cited by 123
- CStarAlgebra.norm_le_iff_le_algebraMapproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- CStarAlgebra.inr_mem_Icc_iff_norm_leproof · cited by 1
- le_iff_norm_sqrt_mul_rpowproof · cited by 1
- CStarAlgebra.norm_sub_mul_self_le_of_inrproof · cited by 0
- CStarAlgebra.nnnorm_le_one_iff_of_nonnegproof · cited by 0
- IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitaryproof · cited by 0