Theorems · Theorem · functional analysis
le_iff_norm_sqrt_mul_sqrt_inv
∀ {A : Type u_1} [inst : CStarAlgebra A] [inst_1 : PartialOrder A] [inst_2 : StarOrderedRing A] {a : A} {b : Aˣ},
0 ≤ a → 0 ≤ ↑b → (a ≤ ↑b ↔ ‖CFC.sqrt a * CFC.sqrt ↑b⁻¹‖ ≤ 1)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 322 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- PartialOrderstatement and proof · cited by 6,410
- Complexstatement · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- one_mulproof · cited by 2,841
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- neg_mulproof · cited by 654
- one_divproof · cited by 624
- StarOrderedRingstatement and proof · cited by 587
- CStarAlgebrastatement and proof · cited by 123
- IsStarNormalstatement · cited by 117
Cited by1
Results whose statement or proof uses this declaration.
- CStarAlgebra.inv_le_invproof · cited by 3