ACTA issues

Spectra of composition operators on weighted Bergman spaces

Matthew A. Pons

Acta Sci. Math. (Szeged) 85:3-4(2019), 539-560

Abstract. 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 MacCluer and Saxe.

DOI: 10.14232/actasm-018-072-7

AMS Subject Classification (1991): 47B33

Keyword(s): composition operator, spectrum, essential spectral radius, weighted Bergman space, Bloch space

Received August 6, 2018 and in final form January 20, 2019. (Registered under 72/2018.)