Theorems · Theorem · functional analysis
IsSelfAdjoint.coe_mem_spectrum_complex
∀ {A : Type u_2} [inst : TopologicalSpace A] [inst_1 : Ring A] [inst_2 : StarRing A] [inst_3 : Algebra ℂ A]
[ContinuousFunctionalCalculus ℂ A IsStarNormal] {a : A} {x : ℝ},
autoParam (IsSelfAdjoint a) IsSelfAdjoint.coe_mem_spectrum_complex._auto_1 → (↑x ∈ spectrum ℂ a ↔ x ∈ spectrum ℝ a)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- 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
- Complexstatement and proof · cited by 5,565
- StarRingstatement and proof · cited by 1,686
- Complex.ofRealstatement and proof · cited by 1,654
- IsSelfAdjointstatement and proof · cited by 545
- Set.image_congrproof · cited by 533
- spectrumstatement and proof · cited by 510
- ContinuousFunctionalCalculusstatement and proof · cited by 331
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