Theorems · Theorem · functional analysis
CStarAlgebra.sqrt_toReal_spectralRadius_star_mul_self_eq_norm
∀ {A : Type u_1} [inst : CStarAlgebra A] (a : A), √(spectralRadius ℂ (star a * a)).toReal = ‖a‖- Defined in
- Mathlib.Analysis.CStarAlgebra.Spectrum
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 290 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CStarAlgebra
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · 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
- Real.sqrtstatement and proof · cited by 545
- CStarAlgebrastatement and proof · cited by 123
- Real.sqrt_sqproof · cited by 36
- spectralRadiusstatement · cited by 36
- CStarAlgebra.toReal_spectralRadius_star_mul_self_eq_norm_sqproof · cited by 2
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