Theorems · Theorem · functional analysis

mem_quasispectrum_iff

∀ {R : Type u_3} {A : Type u_4} [inst : Semifield R] [inst_1 : Ring A] [inst_2 : Algebra R A] {a : A} {x : R},
  x ∈ quasispectrum R a ↔ x = 0 ∨ x ∈ spectrum R a

Defined in

Mathlib.Algebra.Algebra.Spectrum.Quasispectrum

Cited by

2 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemifieldRingAlgebra