Theorems · Theorem · functional analysis
Unitary.norm_sub_one_sq_eq
∀ {A : Type u_1} [inst : CStarAlgebra A] {u : A},
u ∈ unitary A → ∀ {x : ℝ}, IsLeast (Complex.re '' spectrum ℂ u) x → ‖u - 1‖ ^ 2 = 2 * (1 - x)- 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.
Cites45
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Set.ofPredproof · cited by 6,101
- Set.imagestatement and proof · cited by 5,609
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- Submonoidstatement · cited by 3,086
- Nontrivialproof · cited by 2,416
- le_of_ltproof · cited by 1,175
- Complex.restatement and proof · cited by 882
- Set.EqOnproof · cited by 603
- Antitoneproof · cited by 563
- spectrumstatement and proof · cited by 510
Cited by2
Results whose statement or proof uses this declaration.
- selfAdjoint.norm_sq_expUnitary_sub_oneproof · cited by 3
- Unitary.norm_sub_one_lt_two_iffproof · cited by 1