Theorems · Theorem · functional analysis
NNReal.spectrum_nonempty
Deprecated since 2026-03-08Mathlib marks this declaration as deprecated.
∀ {A : Type u_2} [inst : Ring A] [inst_1 : StarRing A] [inst_2 : LE A] [inst_3 : TopologicalSpace A]
[inst_4 : Algebra NNReal A] [ContinuousFunctionalCalculus NNReal A fun x => 0 ≤ x] [Nontrivial A] {a : A},
0 ≤ a → (spectrum NNReal a).Nonempty- Cited by
- 0 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- NNRealstatement and proof · cited by 4,310
- Set.Nonemptystatement · cited by 2,627
- Nontrivialstatement and proof · cited by 2,416
- StarRingstatement and proof · cited by 1,686
- spectrumstatement · cited by 510
- ContinuousFunctionalCalculusstatement and proof · cited by 331
- ContinuousFunctionalCalculus.spectrum_nonemptyproof · cited by 6
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.