Topological structure of the space of composition operators on the Hardy space of Dirichlet series

Abstract

The aim of this paper is to study when two composition operators on the Hilbert space of Dirichlet series with square summable coefficients belong to the same component or when their difference is compact. As a corollary we show that if a linear combination of composition operators with polynomial symbols of degree at most 2 is compact, then each composition operator is compact.

References in corpus (5)

• Approximation numbers of composition operators on the $H^2$ space of Dirichlet series
• Composition Operators on Bohr-Bergman Spaces of Dirichlet Series
• Sharp norm estimates for composition operators and Hilbert-type inequalities
• A mean counting function for Dirichlet series and compact composition operators
• Norms of composition operators on the $H^2$ space of Dirichlet series

Cited by in corpus (1)

• Counting functions for Dirichlet series and compactness of composition operators