Spectral properties of Cesàro-like operators on weighted Bergman spaces
type: Item
instance of: scholarly article
title: Spectral properties of Cesàro-like operators on weighted Bergman spaces
zbMATH Open document ID: 1267.47047
author: S. Ballamoole
author: T. L. Miller
author: V. G. Miller
published in: Journal of Mathematical Analysis and Applications
publication date: 2012-08-01T00:00:00Z
review text: The authors study the spectral properties of certain integral operators acting on weighted Bergman spaces of analytic functions using the representation of the operator as a resolvent of a semigroup. This method was first used by \textit{A. G. Siskakis} in [J. Lond. Math. Soc., II. Ser. 36, No. 1--2, 153--164 (1987; Zbl 0634.47038)] to study composition operators and the Cesàro operator on Hardy spaces. Later, the method was used by several authors in different contexts. The main result of the paper under review is an exact formula for the spectrum of some of the operators they consider.
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 47A11
zbMATH DE Number: 6062852
zbMATH Keywords: integral operator
zbMATH Keywords: weighted Bergman space
zbMATH Keywords: spectral properties
zbMATH Keywords: Cesàro operator
zbMATH Keywords: operator semigroups
zbMATH Keywords: decomposable operators
zbMATH Keywords: generalized scalar operators
zbMATH Keywords: Bishop's property \((\beta )\)
zbMATH Keywords: property \((\beta )_{\varepsilon}\)
reviewed by: Alfonso Montes-Rodriguez
MaRDI profile type: Publication
full work available at URL: j.jmaa.2012.05.012
OpenAlex ID: W2041730029
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DOI: 10.1016/J.JMAA.2012.05.012
description: scientific article; zbMATH DE number 6062852