cfcHom_nnreal_eq_restrict — Mathlib

English

The NNReal version of cfcₙHom equals the nonunital star algebra hom induced by the real restriction on NNReal.

Русский

Версия cfcₙHom на NNReal равна ненулевому звездному алгебра-отображению, индуцированному ограничением на NNReal.

LaTeX

$$$$ cfcₙHom ha = (QuasispectrumRestricts.nnreal_of_nonneg ha).nonUnitalStarAlgHom (cfcₙHom (IsSelfAdjoint.of_nonneg ha)) $$$$

Lean4

theorem cfcHom_nnreal_eq_restrict {a : A} (ha : 0 ≤ a) :
    cfcHom ha = (SpectrumRestricts.nnreal_of_nonneg ha).starAlgHom (cfcHom (IsSelfAdjoint.of_nonneg ha)) := by
  apply (SpectrumRestricts.nnreal_of_nonneg ha).cfcHom_eq_restrict _ isUniformEmbedding_subtype_val

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