Theorems · Theorem · functional analysis
CStarAlgebra.norm_sub_mul_self_le
∀ {A : Type u_2} [inst : CStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A] {x y : A} (z : A),
0 ≤ x → y ∈ Set.Icc x 1 → ∀ {c : ℝ}, 0 ≤ c → ‖star z * (1 - x) * z‖ ≤ c ^ 2 → ‖z - y * z‖ ≤ cA variant of nnnorm_sub_mul_self_le which uses ‖·‖ instead of ‖·‖₊.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 323 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- PartialOrderstatement and proof · cited by 6,410
- Norm.normstatement and proof · cited by 5,413
- Set.Iccstatement and proof · cited by 1,702
- Star.starstatement and proof · cited by 1,082
- StarOrderedRingstatement and proof · cited by 587
- CStarAlgebrastatement and proof · cited by 123
- CStarAlgebra.nnnorm_sub_mul_self_leproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- CStarAlgebra.norm_sub_mul_self_le_of_inrproof · cited by 0