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Spectra of some weighted composition operators on the ball

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We find sufficient conditions for a self-map of the unit ball to converge uniformly under iteration to a fixed point or idempotent on the entire ball. Using these tools, we establish spectral containments for weighted composition operators on Hardy and Bergman spaces of the ball. When the compositional symbol is in the Schur–Agler class, we establish the spectral radii of these weighted composition operators.

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Authors Kaschner, Makdad, Rempfer, Thompson, and Winters were supported by an NSF CURM grant and are grateful to the directors of CURM (Kathryn Leonard, Maria Mercedes Franco) for their counsel. We would also like to thank Michael Jury for his helpful advice.

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Correspondence to Derek Thompson.

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Authors Kaschner, Makdad, Rempfer, Thompson, and Winters were supported by an NSF-CURM Grant.

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Kaschner, S., Le, T., Makdad, C. et al. Spectra of some weighted composition operators on the ball. Acta Sci. Math. (Szeged) 89, 373–387 (2023).

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