On the Bergman space norm of the Cesàro operator
type: Item
instance of: scholarly article
title: On the Bergman space norm of the Cesàro operator
zbMATH Open document ID: 0859.47024
DOI: 10.1007/BF01197596
author: Aristomenis G. Siskasis
published in: Archiv der Mathematik
publication date: 1997-04-09T00:00:00Z
review text: We determine the exact values of the norm and the spectrum for the Cesàro operator \(C_p\) on the Bergman spaces \(A^p\) for \(p\geq 4\) and give estimates for the norm and spectrum for \(1\leq p<4\). For \(p\geq 4\) the values are \(|C_p|=p/2\) and \(\sigma(C_p)= \{z:|z-p/4|\leq p/4\}\). We also find, as a byproduct, the spectra of certain composition operators on \(A^p\). Further a general necessary condition is given for \(C\) to be bounded on certain Banach spaces of analytic functions.
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 30D05
Mathematics Subject Classification ID: 47D03
zbMATH DE Number: 938613
zbMATH Keywords: exact values of the norm
zbMATH Keywords: spectrum
zbMATH Keywords: Cesàro operator
zbMATH Keywords: Bergman spaces
zbMATH Keywords: composition operators
zbMATH Keywords: Banach spaces of analytic functions
MaRDI profile type: Publication
cites work: Q5528082
cites work: Q3222739
cites work: Analytic Toeplitz and Composition Operators
cites work: Q4039882
cites work: The fine spectrum of the Cesàro operator in \(\ell _ p(1<p<\infty)\)
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cites work: Composition operators and classical function theory
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cites work: Semigroups of composition operators in Bergman spaces
cites work: The Cesaro Operator is Bounded on H 1
cites work: Q3999007
full work available at URL: https://doi.org/10.1007/bf01197596
OpenAlex ID: W2072704737
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description: scientific article; zbMATH DE number 938613