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Spectra of composition operators on weighted Bergman spaces. (English) Zbl 1449.47055

Summary: We extend known results on the spectra of composition operators to the weighted Bergman spaces. Our results include a study of the essential spectral radius, a determination of the spectrum when the symbol of the composition operator is univalent and non-automorphic with a fixed point in the disk, and an affirmative answer to a conjecture of B. MacCluer and K. Saxe [Isr. J. Math. 128, 325–354 (2002; Zbl 1024.47009)].

MSC:

47B33 Linear composition operators
30H20 Bergman spaces and Fock spaces
30H30 Bloch spaces

Citations:

Zbl 1024.47009
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