Theorems · Theorem · functional analysis
SpectrumRestricts.nnreal_iff
∀ {A : Type u_1} [inst : Ring A] [inst_1 : Algebra ℝ A] {a : A},
SpectrumRestricts a ⇑ContinuousMap.realToNNReal ↔ ∀ x ∈ spectrum ℝ a, 0 ≤ x- Defined in
- Mathlib.Analysis.Real.Spectrum
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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 · cited by 53,352
- Realstatement and proof · cited by 25,697
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Algebra.algebraMapproof · cited by 4,706
- NNRealstatement and proof · cited by 4,310
- ContinuousMapstatement · cited by 2,491
- spectrumstatement and proof · cited by 510
- NNReal.coe_nonnegproof · cited by 130
- SpectrumRestrictsstatement and proof · cited by 51
- ContinuousMap.realToNNRealstatement and proof · cited by 44
Cited by8
Results whose statement or proof uses this declaration.
- SpectrumRestricts.nnreal_of_nonnegproof · cited by 5
- QuasispectrumRestricts.nnreal_iffproof · cited by 2
- CStarAlgebra.spectralOrderedRingproof · cited by 1
- SpectrumRestricts.smul_of_nonnegproof · cited by 1
- IsSelfAdjoint.sq_spectrumRestrictsproof · cited by 1
- SpectrumRestricts.eq_zero_of_negproof · cited by 1
- SpectrumRestricts.nnreal_iff_spectralRadius_leproof · cited by 1
- ContinuousLinearMap.IsPositive.spectrumRestrictsproof · cited by 0