Theorems · Theorem · functional analysis
QuasispectrumRestricts.nnreal_of_nonneg
∀ {A : Type u_1} [inst : NonUnitalRing A] [inst_1 : Module ℝ A] [IsScalarTower ℝ A A] [SMulCommClass ℝ A A]
[inst_4 : PartialOrder A] [NonnegSpectrumClass ℝ A] {a : A},
0 ≤ a → QuasispectrumRestricts a ⇑ContinuousMap.realToNNReal- Defined in
- Mathlib.Analysis.Real.Spectrum
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- PartialOrderstatement and proof · cited by 6,410
- NNRealstatement · cited by 4,310
- IsScalarTowerstatement and proof · cited by 3,896
- ContinuousMapstatement · cited by 2,491
- SMulCommClassstatement and proof · cited by 1,927
- NonUnitalRingstatement and proof · cited by 422
- NonnegSpectrumClassstatement and proof · cited by 292
- QuasispectrumRestrictsstatement · cited by 50
- ContinuousMap.realToNNRealstatement · cited by 44
Cited by5
Results whose statement or proof uses this declaration.
- cfcₙ_nnreal_eq_realproof · cited by 9
- nonneg_iff_isSelfAdjoint_and_quasispectrumRestrictsproof · cited by 4
- Commute.mul_nonnegproof · cited by 3
- cfcₙHom_nnreal_eq_restrictstatement and proof · cited by 0
- cfcₙ_tsubproof · cited by 0