Theorems · Theorem · functional analysis
Unitary.two_mul_one_sub_le_norm_sub_one_sq
∀ {A : Type u_1} [inst : CStarAlgebra A] {u : A},
u ∈ unitary A → ∀ {z : ℂ}, z ∈ spectrum ℂ u → 2 * (1 - z.re) ≤ ‖u - 1‖ ^ 2- Cited by
- 2 results in Mathlib
- Foundations
- Depth 311 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CStarAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites40
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
- TopologicalSpaceproof · cited by 24,529
- Algebraproof · cited by 11,388
- CommSemiringproof · cited by 10,911
- Ringproof · cited by 7,463
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- Submonoidstatement · cited by 3,086
- StarRingproof · cited by 1,686
- MetricSpaceproof · cited by 1,684
- sub_zeroproof · cited by 938
Cited by2
Results whose statement or proof uses this declaration.
- Unitary.norm_sub_one_lt_two_iffproof · cited by 1
- Unitary.continuousOn_argSelfAdjointproof · cited by 0