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Zeitschrift für Analysis und ihre Anwendungen


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Volume 35, Issue 3, 2016, pp. 267–284
DOI: 10.4171/ZAA/1565

Published online: 2016-09-13

Topological Structure of the Spaces of Composition Operators on Hilbert Spaces of Dirichlet Series

Bingyang Hu[1], Le Hai Khoi[2] and Ruhan Zhao[3]

(1) University of Wisconsin, Madison, USA
(2) Nanyang Technological University (NTU), Singapore, Singapore
(3) SUNY Brockport, USA

In this paper we study some topological properties of the space of bounded composition operators on some Hilbert spaces of Dirichlet series. We fi rst obtain formulas for the norms and essential norms of composition operators and di fferences of composition operators on Hilbert spaces of Dirichlet series. Then we give a characterization of the isolated points in the topological space of bounded composition operators on some Hilbert spaces of Dirichlet series. Finally we obtain sufficient conditions such that two composition operators are in the same path component. We show, among other results, that all compact composition operators are in the same path component. For a certain class of frequencies we give complete description of path components.

Keywords: Hilbert space, entire Dirichlet series, composition operators, isolated point, path component

Hu Bingyang, Khoi Le Hai, Zhao Ruhan: Topological Structure of the Spaces of Composition Operators on Hilbert Spaces of Dirichlet Series. Z. Anal. Anwend. 35 (2016), 267-284. doi: 10.4171/ZAA/1565