Theorems · Theorem · functional analysis
CStarRing.nnnorm_star_mul_self
∀ {E : Type u_2} [inst : NonUnitalNormedRing E] [inst_1 : StarRing E] [CStarRing E] {x : E}, ‖star x * 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement · cited by 4,310
- StarRingstatement and proof · cited by 1,686
- Star.starstatement · cited by 1,082
- NNNorm.nnnormstatement · cited by 952
- NonUnitalNormedRingstatement and proof · cited by 231
- CStarRingstatement and proof · cited by 61
- CStarRing.norm_star_mul_selfproof · cited by 16
Cited by4
Results whose statement or proof uses this declaration.
- DoubleCentralizer.norm_fst_eq_sndproof · cited by 3
- gelfandTransform_isometryproof · cited by 2
- CStarAlgebra.nnnorm_sub_mul_self_leproof · cited by 1
- IsStarNormal.spectralRadius_eq_nnnormproof · cited by 0