Theorems · Theorem · functional analysis

QuasispectrumRestricts.comp

∀ {R₁ : Type u_6} {R₂ : Type u_7} {R₃ : Type u_8} {A : Type u_9} [inst : Semifield R₁] [inst_1 : Field R₂]
  [inst_2 : Field R₃] [inst_3 : NonUnitalRing A] [inst_4 : Module R₁ A] [inst_5 : Module R₂ A] [inst_6 : Module R₃ A]
  [inst_7 : Algebra R₁ R₂] [inst_8 : Algebra R₂ R₃] [inst_9 : Algebra R₁ R₃] [IsScalarTower R₁ R₂ R₃]
  [IsScalarTower R₂ R₃ A] [IsScalarTower R₃ A A] [SMulCommClass R₃ A A] {a : A} {f : R₃ → R₂} {g : R₂ → R₁}
  {e : R₃ → R₁}, g ∘ f = e → QuasispectrumRestricts a f → QuasispectrumRestricts a g → QuasispectrumRestricts a e

Defined in

Mathlib.Algebra.Algebra.Spectrum.Quasispectrum

Cited by

0 results in Mathlib

Foundations

Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemifieldFieldFieldNonUnitalRingModuleModuleModuleAlgebraAlgebraAlgebraIsScalarTowerIsScalarTowerIsScalarTowerSMulCommClass