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Theorems · Theorem · functional analysis

NonnegSpectrumClass.nonneg_of_mem_quasispectrum

∀ {A : Type u_2} [inst : NonUnitalRing A] {𝕜 : Type u_3} [inst_1 : CommSemiring 𝕜] [inst_2 : PartialOrder 𝕜]
  [inst_3 : PartialOrder A] [inst_4 : Module 𝕜 A] [NonnegSpectrumClass 𝕜 A] {a : A},
  0 ≤ a → ∀ {x : 𝕜}, x ∈ quasispectrum 𝕜 a → 0 ≤ x
Defined in
Mathlib.Algebra.Algebra.Spectrum.Quasispectrum
Cited by
0 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NonUnitalRingCommSemiringPartialOrderPartialOrderModuleNonnegSpectrumClass
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Set · cited by 53352SetModule · cited by 20661ModuleCommSemiring · cited by 10911CommSemiringPartialOrder · cited by 6410PartialOrderNonUnitalRing · cited by 422NonUnitalRingquasispectrum · cited by 292quasispectrumNonnegSpectrumClass · cited by 292NonnegSpectrumClassNonnegSpectrumClass.quasispectrum_nonneg_of_nonneg · cited by 9NonnegSpectrumClass.quasi…NonnegSpectrumClass.nonneg_of…CITED BYCITES

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