Theorems · Theorem · functional analysis
Unitary.norm_sub_one_lt_two_iff
∀ {A : Type u_1} [inst : CStarAlgebra A] {u : A}, u ∈ unitary A → (‖u - 1‖ < 2 ↔ -1 ∉ spectrum ℂ u)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 312 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.
Cites34
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
- Set.imageproof · cited by 5,609
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- Submonoidstatement · cited by 3,086
- Nat.cast_oneproof · cited by 2,501
- Nontrivialproof · cited by 2,416
- Nat.cast_zeroproof · cited by 1,870
- le_of_ltproof · cited by 1,175
- Complex.reproof · cited by 882
- LE.le.trans_ltproof · cited by 795
Cited by1
Results whose statement or proof uses this declaration.
- Unitary.spectrum_subset_slitPlane_iff_norm_lt_twoproof · cited by 2