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On the spectrum of the Cesàro operator on spaces of analytic functions

Persson, Anna-Maria LU (2008) In Journal of Mathematical Analysis and Applications 340(2). p.1180-1203
Abstract
This paper concerns the Cesàro operator acting on various spaces of analytic functions on the unit disc. The remarkable fact that this operator is subnormal when acting on the Hardy space H2 has lead to extensive studies of its spectral picture on other spaces of this type. We present some of the methods that have been used to obtain information about the spectrum of the Cesàro operator acting on Hardy and Bergman spaces and give a unified approach to these problems which also yields new results in this direction. In particular, we prove that the Cesàro operator is subdecomposable on H1 and on the standard weighted Bergman spaces , α0.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Cesàro operator, Spaces of analytic functions, Resolvent, Spectrum, Subdecomposable
in
Journal of Mathematical Analysis and Applications
volume
340
issue
2
pages
1180 - 1203
publisher
Elsevier
external identifiers
  • wos:000253133400038
  • scopus:38049052533
ISSN
0022-247X
DOI
10.1016/j.jmaa.2007.09.007
language
English
LU publication?
yes
id
307edb11-8a27-41d1-8074-5d20226322bf (old id 838360)
date added to LUP
2008-01-15 09:14:38
date last changed
2017-09-10 04:21:53
@article{307edb11-8a27-41d1-8074-5d20226322bf,
  abstract     = {This paper concerns the Cesàro operator acting on various spaces of analytic functions on the unit disc. The remarkable fact that this operator is subnormal when acting on the Hardy space H2 has lead to extensive studies of its spectral picture on other spaces of this type. We present some of the methods that have been used to obtain information about the spectrum of the Cesàro operator acting on Hardy and Bergman spaces and give a unified approach to these problems which also yields new results in this direction. In particular, we prove that the Cesàro operator is subdecomposable on H1 and on the standard weighted Bergman spaces , α0.},
  author       = {Persson, Anna-Maria},
  issn         = {0022-247X},
  keyword      = {Cesàro operator,Spaces of analytic functions,Resolvent,Spectrum,Subdecomposable},
  language     = {eng},
  number       = {2},
  pages        = {1180--1203},
  publisher    = {Elsevier},
  series       = {Journal of Mathematical Analysis and Applications},
  title        = {On the spectrum of the Cesàro operator on spaces of analytic functions},
  url          = {http://dx.doi.org/10.1016/j.jmaa.2007.09.007},
  volume       = {340},
  year         = {2008},
}