Theorems · Theorem · functional analysis

ContinuousLinearMap.IsPositive.spectrumRestricts

∀ {𝕜 : Type u_1} {H : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup H] [inst_2 : InnerProductSpace 𝕜 H]
  [CompleteSpace H] [inst_4 : Algebra ℝ (H →L[𝕜] H)] [IsScalarTower ℝ 𝕜 (H →L[𝕜] H)] {f : H →L[𝕜] H},
  f.IsPositive → SpectrumRestricts f ⇑ContinuousMap.realToNNReal

Defined in

Mathlib.Analysis.InnerProductSpace.StarOrder

Cited by

0 results in Mathlib

Foundations

Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceCompleteSpaceAlgebraIsScalarTower