Theorems · Theorem · functional analysis

spectrum.exp_mem_exp

∀ {𝕜 : Type u_1} {A : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedRing A] [inst_2 : NormedAlgebra 𝕜 A] [CompleteSpace A]
  (a : A) {z : 𝕜}, z ∈ spectrum 𝕜 a → NormedSpace.exp z ∈ spectrum 𝕜 (NormedSpace.exp a)

For 𝕜 = ℝ or 𝕜 = ℂ, exp maps the spectrum of a into the spectrum of exp a.

Defined in

Mathlib.Analysis.Normed.Algebra.Spectrum

Cited by

1 results in Mathlib

Foundations

Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedRingNormedAlgebraCompleteSpace