Theorems · Theorem · functional analysis
NNReal.spectralRadius_mem_spectrum
∀ {A : Type u_4} [inst : NormedRing A] [inst_1 : NormedAlgebra ℝ A] [CompleteSpace A] {a : A},
(spectrum ℝ a).Nonempty →
SpectrumRestricts a ⇑ContinuousMap.realToNNReal → (spectralRadius ℝ a).toNNReal ∈ spectrum NNReal a- Defined in
- Mathlib.Analysis.Normed.Algebra.Spectrum
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- ENNRealproof · cited by 9,879
- NNRealstatement and proof · cited by 4,310
- Set.Nonemptystatement and proof · cited by 2,627
- CompleteSpacestatement and proof · cited by 2,532
- ContinuousMapstatement · cited by 2,491
- ENNReal.ofNNRealproof · cited by 1,279
- NNReal.toRealproof · cited by 1,260
- NormedAlgebrastatement and proof · cited by 1,165
- NNNorm.nnnormproof · cited by 952
Cited by2
Results whose statement or proof uses this declaration.
- CStarAlgebra.nnnorm_mem_spectrum_of_nonnegproof · cited by 1
- Real.spectralRadius_mem_spectrumproof · cited by 0