Theorems · Theorem · functional analysis
CStarAlgebra.norm_le_iff_le_algebraMap
∀ {A : Type u_1} [inst : CStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A] (a : A) {r : ℝ},
0 ≤ r → autoParam (0 ≤ a) CStarAlgebra.norm_le_iff_le_algebraMap._auto_1 → (‖a‖ ≤ r ↔ a ≤ (algebraMap ℝ A) r)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 319 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHomstatement · cited by 10,189
- PartialOrderstatement and proof · cited by 6,410
- Norm.normstatement and proof · cited by 5,413
- Algebra.algebraMapstatement · cited by 4,706
- LE.le.transproof · cited by 3,151
- Nontrivialproof · cited by 2,416
- StarOrderedRingstatement and proof · cited by 587
- spectrumproof · cited by 510
- norm_zeroproof · cited by 366
- subsingleton_or_nontrivialproof · cited by 161
Cited by5
Results whose statement or proof uses this declaration.
- CStarAlgebra.norm_le_norm_of_nonneg_of_leproof · cited by 6
- CStarAlgebra.norm_le_one_iff_of_nonnegproof · cited by 6
- CStarAlgebra.mem_Icc_algebraMap_iff_norm_leproof · cited by 2
- CStarAlgebra.nnnorm_le_iff_of_nonnegproof · cited by 1
- CStarAlgebra.norm_le_natCast_iff_of_nonnegproof · cited by 0