Theorems · Theorem · functional analysis

CFC.log_smul

∀ {A : Type u_1} [inst : NormedRing A] [inst_1 : StarRing A] [inst_2 : NormedAlgebra ℝ A]
  [inst_3 : ContinuousFunctionalCalculus ℝ A IsSelfAdjoint] {r : ℝ} (a : A),
  (∀ x ∈ spectrum ℝ a, x ≠ 0) →
    r ≠ 0 →
      autoParam (IsSelfAdjoint a) CFC.log_smul._auto_1 → CFC.log (r • a) = (algebraMap ℝ A) (Real.log r) + CFC.log a

Defined in

Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog.Basic

Cited by

0 results in Mathlib

Foundations

Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedRingStarRingNormedAlgebraContinuousFunctionalCalculus