OAI/Analysis/BoundedHochschild/NormalOrbitInvariance.lean

GitHub source file

8 declarations, 0 contain sorry, 0 declared as axioms

Convexity and invariance of the compact normal-state orbit.

  1. def OAI.BoundedHochschild.KadisonRingrose.weakUnitaryPullback line 23

    Source documentation

    Unitary pullback is weak-star continuous.

    def weakUnitaryPullback (u : unitary M) : WeakDual ℂ M →L[ℂ] WeakDual ℂ M where
…
  2. lemma OAI.BoundedHochschild.KadisonRingrose.unitaryOrbitHull_invariant line 30
  3. lemma OAI.BoundedHochschild.KadisonRingrose.weakOrbitClosure_invariant line 44
  4. lemma OAI.BoundedHochschild.KadisonRingrose.weakOrbitClosure_convex line 53
  5. def OAI.BoundedHochschild.KadisonRingrose.weakPredualRealMap line 70

    Source documentation

    The weak predual embedding is real-linear.

    def weakPredualRealMap (e : StrongDual ℂ X ≃ₗᵢ⋆[ℂ] M) :
    WeakSpace ℂ X →ₗ[ℝ] WeakDual ℂ M where
…
  6. lemma OAI.BoundedHochschild.KadisonRingrose.weakPredualOrbit_convex line 90
  7. lemma OAI.BoundedHochschild.KadisonRingrose.weakPredualOrbit_invariant line 102
  8. lemma OAI.BoundedHochschild.KadisonRingrose.weakFunctionalClosure_eval_eq line 118