Theorems · Theorem · ring theory
IsSelfAdjoint.star_mul_self
∀ {R : Type u_1} [inst : Mul R] [inst_1 : StarMul R] (x : R), IsSelfAdjoint (star x * x)- Defined in
- Mathlib.Algebra.Star.SelfAdjoint
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Star.starstatement and proof · cited by 1,082
- IsSelfAdjointstatement · cited by 545
- StarMulstatement and proof · cited by 195
- star_starproof · cited by 135
- StarMul.star_mulproof · cited by 72
Cited by12
Results whose statement or proof uses this declaration.
- IsSelfAdjoint.mul_star_selfproof · cited by 2
- NonUnitalStarAlgHom.nnnorm_apply_leproof · cited by 2
- gelfandTransform_isometryproof · cited by 2
- NonUnitalStarAlgHom.norm_mapproof · cited by 2
- CStarAlgebra.toReal_spectralRadius_star_mul_self_eq_norm_sqproof · cited by 2
- ContinuousLinearMap.isStarNormal_iff_norm_eq_adjointproof · cited by 2
- ContinuousLinearMap.IsIdempotentElem.isSelfAdjoint_iff_isStarNormalproof · cited by 2
- CStarAlgebra.spectralOrderedRingproof · cited by 1
- CStarAlgebra.star_left_conjugate_le_norm_smulproof · cited by 1
- StarSubalgebra.coe_isUnitproof · cited by 1
- spectrum_star_mul_self_nonnegproof · cited by 1
- IsStarNormal.spectralRadius_eq_nnnormproof · cited by 0