Theorems · Theorem · functional analysis
IsSelfAdjoint.val_re_map_spectrum
∀ {A : Type u_1} [inst : CStarAlgebra A] {a : A},
IsSelfAdjoint a → spectrum ℂ a = Complex.ofReal ∘ Complex.re '' spectrum ℂ aThe spectrum of a selfadjoint is real
- Defined in
- Mathlib.Analysis.CStarAlgebra.Spectrum
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 182 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- Set.imagestatement and proof · cited by 5,609
- Complexstatement and proof · cited by 5,565
- le_antisymmproof · cited by 2,068
- Complex.ofRealstatement and proof · cited by 1,654
- Complex.restatement and proof · cited by 882
- IsSelfAdjointstatement and proof · cited by 545
- spectrumstatement and proof · cited by 510
- CStarAlgebrastatement and proof · cited by 123
- IsSelfAdjoint.mem_spectrum_eq_reproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- selfAdjoint.val_re_map_spectrumproof · cited by 0