English
The core cfc is defined as the eta-helper of the wrapped construction, matching the external delta-definition up to the chosen encoding.
Русский
Ядро cfc задано через η-хелпер и обёртку, совпадая с внешним определением δ в принятый способ кодирования.
LaTeX
$$cfc f a = η_helper Eq✝ @cfc.{} @(delta% @definition✝)$$
Lean4
/-- This is the *continuous functional calculus* of an element `a : A` applied to bare functions.
When either `a` does not satisfy the predicate `p` (i.e., `a` is not `IsStarNormal`,
`IsSelfAdjoint`, or `0 ≤ a` when `R` is `ℂ`, `ℝ`, or `ℝ≥0`, respectively), or when `f : R → R` is
not continuous on the spectrum of `a`, then `cfc f a` returns the junk value `0`.
This is the primary declaration intended for widespread use of the continuous functional calculus,
and all the API applies to this declaration. For more information, see the module documentation
for `Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital`. -/
noncomputable def cfc :=
val_proj @wrapped✝.{}
