linearIsometryBoundedOfCompact_of_compact_toEquiv

English

If α is compact, then C(α, β) carries a NormedStarGroup structure, i.e., star operation is continuous and compatible with the norm.

Русский

Пусть α компактно; тогда C(α, β) образует NormedStarGroup: операция звезды совместима с нормой и непрерывна.

LaTeX

$$NormedStarGroup (C(α, β)) with norm_star_le and star-additions as in the compact setting.$$

Lean4

@[simp]
theorem linearIsometryBoundedOfCompact_of_compact_toEquiv :
    (linearIsometryBoundedOfCompact α E 𝕜).toLinearEquiv.toEquiv = equivBoundedOfCompact α E :=
  rfl

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