JournalszaaVol. 35, No. 3pp. 267–284

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

  • Bingyang Hu

    University of Wisconsin, Madison, USA
  • Le Hai Khoi

    Nanyang Technological University (NTU), Singapore, Singapore
  • Ruhan Zhao

    SUNY Brockport, USA
Topological Structure of the Spaces of Composition Operators on Hilbert Spaces of Dirichlet Series cover
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Abstract

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.

Cite this article

Bingyang Hu, Le Hai Khoi, Ruhan Zhao, Topological Structure of the Spaces of Composition Operators on Hilbert Spaces of Dirichlet Series. Z. Anal. Anwend. 35 (2016), no. 3, pp. 267–284

DOI 10.4171/ZAA/1565