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Theorems · Theorem · functional analysis

quasispectrum.nonempty

∀ (R : Type u_1) {A : Type u_2} [inst : CommSemiring R] [inst_1 : NonUnitalRing A] [inst_2 : Module R A] [Nontrivial R]
  (a : A), (quasispectrum R a).Nonempty
Defined in
Mathlib.Algebra.Algebra.Spectrum.Quasispectrum
Cited by
1 results in Mathlib
Foundations
Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiringNonUnitalRingModuleNontrivial
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsGreatest.norm_cfcₙ · cited by 5IsGreatest.norm_cfcₙModule · cited by 20661ModuleCommSemiring · cited by 10911CommSemiringSet.Nonempty · cited by 2627Set.NonemptyNontrivial · cited by 2416NontrivialNonUnitalRing · cited by 422NonUnitalRingquasispectrum · cited by 292quasispectrumSet.nonempty_of_mem · cited by 19Set.nonempty_of_memquasispectrum.zero_mem · cited by 13quasispectrum.zero_memquasispectrum.nonemptyCITED BYCITES

Cites8

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Cited by1

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