Theorems · Theorem · functional analysis
CStarRing.norm_coe_unitary_mul
∀ {E : Type u_2} [inst : NormedRing E] [inst_1 : StarRing E] [CStarRing E] (U : ↥(unitary E)) (A : E), ‖↑U * A‖ = ‖A‖- Defined in
- Mathlib.Analysis.CStarAlgebra.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 120 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.
Cites15
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
- one_mulproof · cited by 2,841
- StarRingstatement and proof · cited by 1,686
- mul_assocproof · cited by 1,667
- Star.starproof · cited by 1,082
- NormedRingstatement and proof · cited by 924
- norm_nonnegproof · cited by 725
- sqproof · cited by 280
- unitarystatement and proof · cited by 207
- StarMul.star_mulproof · cited by 72
Cited by5
Results whose statement or proof uses this declaration.
- Unitary.mulLeftproof · cited by 7
- CStarRing.norm_mul_coe_unitaryproof · cited by 2
- Unitary.isPathConnected_ballproof · cited by 0
- CStarRing.norm_unitary_smulproof · cited by 0
- CStarRing.norm_mem_unitary_mulproof · cited by 0