Theorems · Theorem · functional analysis
norm_star
∀ {E : Type u_2} [inst : SeminormedAddCommGroup E] [inst_1 : StarAddMonoid E] [NormedStarGroup E] (x : E),
‖star x‖ = ‖x‖- Defined in
- Mathlib.Analysis.CStarAlgebra.Basic
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 101 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
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- le_antisymmproof · cited by 2,068
- Star.starstatement and proof · cited by 1,082
- StarAddMonoidstatement and proof · cited by 296
- star_starproof · cited by 135
- NormedStarGroupstatement and proof · cited by 54
- NormedStarGroup.norm_star_leproof · cited by 1
Cited by17
Results whose statement or proof uses this declaration.
- CStarRing.norm_star_mul_selfproof · cited by 16
- starₗᵢproof · cited by 6
- star_isometryproof · cited by 6
- CStarRing.norm_self_mul_starproof · cited by 4
- nnnorm_starproof · cited by 4
- OrthonormalBasis.sum_sq_norm_inner_rightproof · cited by 3
- realPart.norm_leproof · cited by 2
- MeasureTheory.eLpNorm_starproof · cited by 2
- ContinuousLinearMap.opNorm_mul_flip_applyproof · cited by 2
- CStarRing.norm_mul_coe_unitaryproof · cited by 2
- Memℓp.star_memproof · cited by 1
- CFC.norm_mul_mul_star_self_of_nonnegproof · cited by 1