Theorems · Theorem · functional analysis
CStarRing.norm_mul_coe_unitary
∀ {E : Type u_2} [inst : NormedRing E] [inst_1 : StarRing E] [CStarRing E] (A : E) (U : ↥(unitary E)), ‖A * ↑U‖ = ‖A‖- Defined in
- Mathlib.Analysis.CStarAlgebra.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedRingStarRingCStarRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- Submonoidstatement · cited by 3,086
- StarRingstatement and proof · cited by 1,686
- Star.starproof · cited by 1,082
- NormedRingstatement and proof · cited by 924
- unitarystatement and proof · cited by 207
- StarMul.star_mulproof · cited by 72
- CStarRingstatement and proof · cited by 61
- norm_starproof · cited by 16
- CStarRing.norm_coe_unitary_mulproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Unitary.mulRightproof · cited by 9
- Unitary.norm_sub_eqproof · cited by 1
- CStarRing.norm_mul_mem_unitaryproof · cited by 0