Theorems · Theorem · functional analysis
SpectrumRestricts.eq_zero_of_neg
∀ {A : Type u_1} [inst : CStarAlgebra A] {a : A},
IsSelfAdjoint a →
SpectrumRestricts a ⇑ContinuousMap.realToNNReal → SpectrumRestricts (-a) ⇑ContinuousMap.realToNNReal → a = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 311 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CStarAlgebra
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 and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NNRealstatement · cited by 4,310
- ContinuousMapstatement · cited by 2,491
- Nat.cast_zeroproof · cited by 1,870
- neg_negproof · cited by 960
- IsSelfAdjointstatement and proof · cited by 545
- spectrumproof · cited by 510
- CStarAlgebrastatement and proof · cited by 123
- SpectrumRestrictsstatement and proof · cited by 51
- ContinuousMap.realToNNRealstatement and proof · cited by 44
- Set.subset_singleton_iffproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- spectrum_star_mul_self_nonnegproof · cited by 1