Theorems · Theorem · functional analysis
SpectrumRestricts.nnreal_of_nonneg
∀ {A : Type u_1} [inst : Ring A] [inst_1 : Algebra ℝ A] [inst_2 : PartialOrder A] [NonnegSpectrumClass ℝ A] {a : A},
0 ≤ a → SpectrumRestricts a ⇑ContinuousMap.realToNNReal- Defined in
- Mathlib.Analysis.Real.Spectrum
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 123 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.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- NNRealstatement · cited by 4,310
- ContinuousMapstatement · cited by 2,491
- NonnegSpectrumClassstatement and proof · cited by 292
- SpectrumRestrictsstatement · cited by 51
- ContinuousMap.realToNNRealstatement · cited by 44
- SpectrumRestricts.nnreal_iffproof · cited by 8
- spectrum_nonneg_of_nonnegproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- cfc_nnreal_eq_realproof · cited by 9
- CStarAlgebra.nnnorm_mem_spectrum_of_nonnegproof · cited by 1
- cfc_tsubproof · cited by 1
- cfcHom_nnreal_eq_restrictstatement and proof · cited by 0
- coe_mem_spectrum_real_of_nonnegproof · cited by 0