Theorems · Theorem · functional analysis
IsSelfAdjoint.spectralRadius_eq_nnnorm
∀ {A : Type u_1} [inst : CStarAlgebra A] {a : A}, IsSelfAdjoint a → spectralRadius ℂ a = ↑‖a‖₊- Defined in
- Mathlib.Analysis.CStarAlgebra.Spectrum
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 287 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.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement and proof · cited by 9,879
- Filterproof · cited by 8,121
- Complexstatement and proof · cited by 5,565
- nhdsproof · cited by 5,554
- NNRealproof · cited by 4,310
- Filter.Tendstoproof · cited by 3,814
- Filter.atTopproof · cited by 2,405
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- NNNorm.nnnormstatement and proof · cited by 952
- one_divproof · cited by 624
- Filter.Tendsto.compproof · cited by 560
- IsSelfAdjointstatement and proof · cited by 545
Cited by7
Results whose statement or proof uses this declaration.
- NonUnitalStarAlgHom.nnnorm_apply_leproof · cited by 2
- gelfandTransform_isometryproof · cited by 2
- SpectrumRestricts.nnreal_iff_nnnormproof · cited by 2
- IsSelfAdjoint.toReal_spectralRadius_eq_normproof · cited by 2
- CStarAlgebra.nnnorm_mem_spectrum_of_nonnegproof · cited by 1
- IsSelfAdjoint.toReal_spectralRadius_complex_eq_normproof · cited by 1
- IsStarNormal.spectralRadius_eq_nnnormproof · cited by 0