Theorems · Theorem · functional analysis
SpectrumRestricts.nnreal_iff_spectralRadius_le
∀ {A : Type u_3} [inst : Ring A] [inst_1 : Algebra ℝ A] {a : A} {t : NNReal},
spectralRadius ℝ a ≤ ↑t →
(SpectrumRestricts a ⇑ContinuousMap.realToNNReal ↔ spectralRadius ℝ ((algebraMap ℝ A) ↑t - a) ≤ ↑t)- Defined in
- Mathlib.Analysis.Normed.Algebra.Spectrum
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites39
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
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- ENNRealstatement · cited by 9,879
- Ringstatement and proof · cited by 7,463
- Algebra.algebraMapstatement and proof · cited by 4,706
- NNRealstatement and proof · cited by 4,310
- LE.le.transproof · cited by 3,151
- ContinuousMapstatement · cited by 2,491
- iSupproof · cited by 2,415
Cited by1
Results whose statement or proof uses this declaration.
- SpectrumRestricts.nnreal_iff_nnnormproof · cited by 2