Topological structure of the space of composition operators on the Hardy space of Dirichlet series
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 s...
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| Vydané v: | Journal of functional analysis Ročník 289; číslo 11; s. 111134 |
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01.12.2025
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| 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. |
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| AbstractList | 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. |
| ArticleNumber | 111134 |
| Author | Yao, Xingxing Wang, Maofa Bayart, Frédéric |
| Author_xml | – sequence: 1 givenname: Frédéric surname: Bayart fullname: Bayart, Frédéric email: frederic.bayart@uca.fr organization: Laboratoire de Mathématiques Blaise Pascal UMR 6620 CNRS, Université Clermont Auvergne, Campus universitaire des Cézeaux, 3 place Vasarely, 63178 Aubière Cedex, France – sequence: 2 givenname: Maofa surname: Wang fullname: Wang, Maofa email: mfwang.math@whu.edu.cn organization: School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China – sequence: 3 givenname: Xingxing orcidid: 0000-0002-2725-943X surname: Yao fullname: Yao, Xingxing email: xxyaom.ath@wit.edu.cn organization: School of Mathematics and Physics, Wuhan Institute of Technology, Wuhan 430205, China |
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| Cites_doi | 10.1007/s00605-002-0470-7 10.1016/j.aim.2021.107775 10.1090/S0002-9939-1981-0593463-0 10.5186/aasfm.2016.4104 10.7900/jot.2020mar23.2288 10.1007/s00209-015-1449-0 10.1090/S0002-9947-07-04166-9 10.1016/j.jfa.2016.08.006 10.1007/BF02819453 10.1016/S0022-247X(03)00004-0 10.1112/blms.12092 10.1215/S0012-7094-97-08601-4 10.2140/pjm.2017.291.81 10.1016/j.jfa.2019.108320 10.1016/j.jfa.2019.108393 10.4064/sm226-1-2 10.1007/BF01194560 10.7153/jmi-07-38 10.1016/j.jfa.2004.01.003 10.1016/j.jfa.2014.11.022 10.2140/pjm.1990.145.117 10.1307/mmj/1030132413 10.1016/j.jmaa.2015.01.010 |
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| Keywords | secondary Topological structure Dirichlet series Linear combination Composition operator primary 2010 Mathematics Subject Classification. Primary 47B33 topological structure Secondary 30B50 linear combination compactness 46E15 Composition operator |
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| Title | Topological structure of the space of composition operators on the Hardy space of Dirichlet series |
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