Theorems · Theorem · functional analysis

StarAlgEquiv.eq_linearIsometryEquivConjStarAlgEquiv

∀ {𝕜 : Type u_1} {V : Type u_2} {W : Type u_3} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup V]
  [inst_2 : InnerProductSpace 𝕜 V] [inst_3 : CompleteSpace V] [inst_4 : NormedAddCommGroup W]
  [inst_5 : InnerProductSpace 𝕜 W] [inst_6 : CompleteSpace W] (f : (V →L[𝕜] V) ≃⋆ₐ[𝕜] W →L[𝕜] W),
  Continuous ⇑f → ∃ U, f = U.conjStarAlgEquiv

The ⋆-algebra equivalence version of ContinuousAlgEquiv.eq_continuousLinearEquivConjContinuousAlgEquiv. TODO: remove the hypothesis Continuous f, as star-algebra equivalences between endomorphisms are automatically continuous.

Defined in

Mathlib.Analysis.Normed.Operator.ContinuousAlgEquiv

Cited by

0 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceCompleteSpaceNormedAddCommGroupInnerProductSpaceCompleteSpace