Theorems · Theorem · functional analysis
CStarRing.norm_self_mul_star
∀ {E : Type u_2} [inst : NonUnitalNormedRing E] [inst_1 : StarRing E] [CStarRing E] {x : E}, ‖x * star x‖ = ‖x‖ * ‖x‖- Defined in
- Mathlib.Analysis.CStarAlgebra.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- StarRingstatement and proof · cited by 1,686
- Star.starstatement and proof · cited by 1,082
- NonUnitalNormedRingstatement and proof · cited by 231
- star_starproof · cited by 135
- CStarRingstatement and proof · cited by 61
- norm_starproof · cited by 16
- CStarRing.norm_star_mul_selfproof · cited by 16
Cited by4
Results whose statement or proof uses this declaration.
- CStarAlgebra.inv_le_invproof · cited by 3
- CStarModule.norm_inner_leproof · cited by 2
- CStarRing.nnnorm_self_mul_starproof · cited by 1
- CStarAlgebra.mul_star_le_algebraMap_norm_sqproof · cited by 0