Illinois Journal of Mathematics

Compact composition operators on a Hilbert space of Dirichlet series

Frédéric Bayart

Full-text: Open access

Abstract

We study the compactness of composition operators on the Hilbert space of Dirichlet series with square summable coefficients. In particular, we give some necessary and sufficient conditions for compactness. We also describe the spectrum of such operators, and we extend our work to some weighted spaces.

Article information

Source
Illinois J. Math., Volume 47, Number 3 (2003), 725-743.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138190

Digital Object Identifier
doi:10.1215/ijm/1258138190

Mathematical Reviews number (MathSciNet)
MR2007233

Zentralblatt MATH identifier
1059.47023

Subjects
Primary: 47B33: Composition operators
Secondary: 30B50: Dirichlet series and other series expansions, exponential series [See also 11M41, 42-XX] 47B07: Operators defined by compactness properties

Citation

Bayart, Frédéric. Compact composition operators on a Hilbert space of Dirichlet series. Illinois J. Math. 47 (2003), no. 3, 725--743. doi:10.1215/ijm/1258138190. https://projecteuclid.org/euclid.ijm/1258138190


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