Topological structure of the spaces of composition operators on Hilbert spaces of Dirichlet series
type: Item
instance of: scholarly article
title: Topological structure of the spaces of composition operators on Hilbert spaces of Dirichlet series
zbMATH Open document ID: 1362.47009
DOI: 10.4171/ZAA/1565
author: Bingyang Hu
author: Le Hai Khoi
author: Ruhan Zhao
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2016-10-25T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 47B33
Mathematics Subject Classification ID: 46E20
Mathematics Subject Classification ID: 30B50
zbMATH DE Number: 6643051
zbMATH Keywords: Hilbert space
zbMATH Keywords: entire Dirichlet series
zbMATH Keywords: composition operators
zbMATH Keywords: isolated point
zbMATH Keywords: path component
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/zaa/1565
OpenAlex ID: W2519193902
description: scientific article; zbMATH DE number 6643051