Theorems · Theorem · functional analysis
CStarAlgebra.mem_Icc_algebraMap_iff_norm_le
∀ {A : Type u_1} [inst : CStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A] {x : A} {r : ℝ},
0 ≤ r → (x ∈ Set.Icc 0 ((algebraMap ℝ A) r) ↔ 0 ≤ x ∧ ‖x‖ ≤ r)- Cited by
- 2 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- 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
- Set.Iccstatement · cited by 1,702
- StarOrderedRingstatement and proof · cited by 587
- CStarAlgebrastatement and proof · cited by 123
- Set.mem_Iccproof · cited by 46
- CStarAlgebra.norm_le_iff_le_algebraMapproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- CStarAlgebra.mem_Icc_iff_norm_le_oneproof · cited by 1
- CStarAlgebra.mem_Icc_algebraMap_iff_nnnorm_leproof · cited by 0