Theorems · Theorem · functional analysis
CStarAlgebra.toReal_spectralRadius_star_mul_self_eq_norm_sq
∀ {A : Type u_1} [inst : CStarAlgebra A] (a : A), (spectralRadius ℂ (star a * a)).toReal = ‖a‖ ^ 2- Defined in
- Mathlib.Analysis.CStarAlgebra.Spectrum
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 289 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CStarAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Complexstatement · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- Star.starstatement · cited by 1,082
- ENNReal.toRealstatement · cited by 859
- pow_twoproof · cited by 150
- CStarAlgebrastatement and proof · cited by 123
- spectralRadiusstatement · cited by 36
- CStarRing.norm_star_mul_selfproof · cited by 16
- IsSelfAdjoint.star_mul_selfproof · cited by 12
- IsSelfAdjoint.toReal_spectralRadius_complex_eq_normproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- CStarAlgebra.toReal_spectralRadius_self_mul_star_eq_norm_sqproof · cited by 1
- CStarAlgebra.sqrt_toReal_spectralRadius_star_mul_self_eq_normproof · cited by 0