Journal of Operator Theory

Volume 88, Issue 1, Summer 2022 pp. 61-84.

Compact linear combinations of composition operators over the unit ball

Authors: Xin Guo (1), Maofa Wang (2)
Author institution: (1) School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
(2) School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Summary: In this paper, we study the compactness of any finite linear combination of composition operators with general symbols on weighted Bergman spaces over the unit ball in terms of a power type criterion. The strategy of the proof involves the subtle connection of composition operator theory between weighted Bergman spaces and Korenblum spaces.

DOI: http://dx.doi.org/10.7900/jot.2020nov28.2310
Keywords: composition operator, linear combination, compact operator, weighted Bergman space, Korenblum space

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