Theorems · Theorem · functional analysis
spectrum.spectralRadius_le_nnnorm
∀ {𝕜 : Type u_1} {A : Type u_2} [inst : NormedField 𝕜] [inst_1 : NormedRing A] [inst_2 : NormedAlgebra 𝕜 A]
[CompleteSpace A] [NormOneClass A] (a : A), spectralRadius 𝕜 a ≤ ↑‖a‖₊- Defined in
- Mathlib.Analysis.Normed.Algebra.Spectrum
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement · cited by 9,879
- CompleteSpacestatement and proof · cited by 2,532
- ENNReal.ofNNRealstatement · cited by 1,279
- NormedAlgebrastatement and proof · cited by 1,165
- NormedFieldstatement and proof · cited by 1,084
- NNNorm.nnnormstatement · cited by 952
- NormedRingstatement and proof · cited by 924
- spectrumproof · cited by 510
- NormOneClassstatement and proof · cited by 136
- iSup₂_leproof · cited by 96
- spectralRadiusstatement · cited by 36
- spectrum.norm_le_norm_of_memproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.spectralRadius_eq_nnnormproof · cited by 1