Commit 2025-11-15 00:04 a75af2d3
View on Github →feat: generalize continuity results for the continuous functional calculus (#30594)
Under suitable conditions x ↦ cfc f (a x) is continuous. Previously these conditions were that there was a single compact set on which f was continuous, and which contained the spectra of all a x. However, this is a bit too stringent for some purposes and so we generalize it here. In particular, it suffices that the spectra a x are covered by a family of compact sets s x (on each of which f is continuous) satisfying the property that each s x₀ contains the spectra a x for x sufficiently close to x₀.