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• W2963950307 abstract "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 Ω‾. Our typical result shows that under some extra conditions, if the closed unit disc is complete K′-spectral for φ(T) for every φ∈Φ, then Ω‾ 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 K′-spectral sets for T is again K-spectral for some K≥K′. 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 ∂Ω. As a key tool, we use the results from our previous paper [11] on traces of analytic uniform algebras." @default.
• W2963950307 created "2019-07-30" @default.
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• W2963950307 date "2017-08-01" @default.
• W2963950307 modified "2023-09-26" @default.
• W2963950307 title "Tests for complete K-spectral sets" @default.
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• W2963950307 doi "https://doi.org/10.1016/j.jfa.2017.03.008" @default.
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