quasispectrumRestricts_iff_spectrumRestricts_inr

English

QuasispectrumRestricts a f is equivalent to SpectrumRestricts (a : Unitization S A) f.

Русский

QuasispectrumRestricts a f эквивалентно SpectrumRestricts (a : Unitization S A) f.

LaTeX

$$$ QuasispectrumRestricts a f \\iff SpectrumRestricts (a : Unitization S A) f $$$

Lean4

theorem quasispectrumRestricts_iff_spectrumRestricts_inr (S : Type*) {R A : Type*} [Semifield R] [Field S]
    [NonUnitalRing A] [Algebra R S] [Module R A] [Module S A] [IsScalarTower S A A] [SMulCommClass S A A]
    [IsScalarTower R S A] {a : A} {f : S → R} :
    QuasispectrumRestricts a f ↔ SpectrumRestricts (a : Unitization S A) f := by
  rw [quasispectrumRestricts_iff, spectrumRestricts_iff, ← Unitization.quasispectrum_eq_spectrum_inr']

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