Theorems · Theorem · functional analysis
IsSelfAdjoint.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 : TopologicalSpace A] [inst_3 : Algebra ℝ A]
[ContinuousFunctionalCalculus ℝ A IsSelfAdjoint] [Nontrivial A] {a : A}, IsSelfAdjoint a → (spectrum ℝ a).Nonempty- Cited by
- 0 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Set.Nonemptystatement · cited by 2,627
- Nontrivialstatement and proof · cited by 2,416
- StarRingstatement and proof · cited by 1,686
- IsSelfAdjointstatement and proof · cited by 545
- spectrumstatement · cited by 510
- ContinuousFunctionalCalculusstatement and proof · cited by 331
- ContinuousFunctionalCalculus.spectrum_nonemptyproof · cited by 6
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