Theorems · Theorem · functional analysis

QuasispectrumRestricts.apply_mem

∀ {R : Type u_3} {S : Type u_4} {A : Type u_5} [inst : Semifield R] [inst_1 : Field S] [inst_2 : NonUnitalRing A]
  [inst_3 : Module R A] [inst_4 : Module S A] [inst_5 : Algebra R S] {a : A} {f : S → R} [IsScalarTower S A A]
  [SMulCommClass S A A] [IsScalarTower R S A],
  QuasispectrumRestricts a f → ∀ {s : S}, s ∈ quasispectrum S a → f s ∈ quasispectrum R a

Defined in

Mathlib.Algebra.Algebra.Spectrum.Quasispectrum

Cited by

2 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemifieldFieldNonUnitalRingModuleModuleAlgebraIsScalarTowerSMulCommClassIsScalarTower