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Journal of Operator Theory

Volume 86, Issue 1, Summer 2021  pp. 231-251.

Linear combinations of composition operators with linear symbols on a Hilbert space of Dirichlet series

Authors:  Frederic Bayart (1), Maofa Wang (2), Xingxing Yao (3)
Author institution:(1) Laboratoire de Mathematiques Blaise Pascal UMR 6620 CNRS, Universite Clermont Auvergne, Campus universitaire des Cezeaux, 3 place Vasarely, 63178 Aubiere Cedex, France
(2) School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
(3) School of Mathematics and Physics, Wuhan Institute of Technology, Wuhan 430205, China

Summary: On the Hilbert space of Dirichlet series with square summable coefficients, we show that the linear combinations of two composition operators induced by linear symbols are compact only when each one of them is compact. Moreover, such rigid behavior holds partially for some more general symbols.

Keywords: linear combination, composition operator, Dirichlet series

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