Theorems · Theorem · functional analysis
quasispectrum.mem_of_not_quasiregular
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : NonUnitalRing A] [inst_2 : Module R A] (a : A)
{r : Rˣ}, ¬IsQuasiregular (-(r⁻¹ • a)) → ↑r ∈ quasispectrum R a- Cited by
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- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- CommSemiringstatement and proof · cited by 10,911
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- IsUnitproof · cited by 1,602
- NonUnitalRingstatement and proof · cited by 422
- quasispectrumstatement · cited by 292
- IsQuasiregularstatement and proof · cited by 18
- IsUnit.unit_of_val_unitsproof · cited by 5
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