Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772154 | Journal of Functional Analysis | 2017 | 36 Pages |
Let Φ be a family of functions analytic in some neighborhood of a complex domain Ω, and let T be a Hilbert space operator whose spectrum is contained in Ωâ¾. Our typical result shows that under some extra conditions, if the closed unit disc is complete Kâ²-spectral for Ï(T) for every ÏâΦ, then Ω⾠is complete K-spectral for T for some constant K. In particular, we prove that under a geometric transversality condition, the intersection of finitely many Kâ²-spectral sets for T is again K-spectral for some Kâ¥Kâ². These theorems generalize and complement results by Mascioni, Stessin, Stampfli, Badea-Beckermann-Crouzeix and others. We also extend to non-convex domains a result by Putinar and Sandberg on the existence of a skew dilation of T to a normal operator with spectrum in âΩ. As a key tool, we use the results from our previous paper [11] on traces of analytic uniform algebras.