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Hankel operators and atomic decompositions in vector-valued Bergman spaces

Constantin, Olivia LU (2005) In Doctoral Theses in Mathematical Sciences 2005:9.
Abstract
Abstract



This thesis consists of the following three papers



Paper I. Hankel operators on Bergman spaces and similarity to contractions.



In this paper we consider Foguel-Hankel operators on vector-valued Bergman spaces. Such operators defined on Hardy spaces play a central role in the famous example by Pisier of a polynomially bounded operator which is not similar to a contraction. On Bergman spaces we encounter a completely different behaviour; power boundedness, polynomial boundedness and similarity to a contraction are all equivalent for this class of operators.



Paper II. Weak product decompositions and Hankel operators on vector-valued Bergman spaces.

... (More)
Abstract



This thesis consists of the following three papers



Paper I. Hankel operators on Bergman spaces and similarity to contractions.



In this paper we consider Foguel-Hankel operators on vector-valued Bergman spaces. Such operators defined on Hardy spaces play a central role in the famous example by Pisier of a polynomially bounded operator which is not similar to a contraction. On Bergman spaces we encounter a completely different behaviour; power boundedness, polynomial boundedness and similarity to a contraction are all equivalent for this class of operators.



Paper II. Weak product decompositions and Hankel operators on vector-valued Bergman spaces.



We obtain weak product decomposition theorems, which represent the Bergman space analogues to Sarason's theorem for operator-valued Hardy spaces, respectively, to the Ferguson-Lacey theorem for Hardy spaces on product domains. We also characterize the compact Hankel operators on vector-valued Bergman spaces.



Paper III. Discretizations of integral operators and atomic decompositions in vector-valued Bergman spaces.



We prove a general atomic decomposition theorem for weighted vector-valued Bergman spaces, which has applications to duality problems and to the study of compact Toeplitz type operator (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Professor Pott, Sandra, University of Glasgow
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Mathematics, Matematik, Hankel operators, similarity to contractions, atomic decompositions
in
Doctoral Theses in Mathematical Sciences
volume
2005:9
pages
71 pages
publisher
KFS AB
defense location
Sölvegatan 18, Sal MH:C
defense date
2005-10-14 10:15:00
ISSN
1404-0034
ISBN
91-628-6625-7
language
English
LU publication?
yes
id
3976d9ef-19ba-4869-9340-f9f72d03721e (old id 545435)
date added to LUP
2016-04-01 15:46:22
date last changed
2025-04-04 13:53:44
@phdthesis{3976d9ef-19ba-4869-9340-f9f72d03721e,
  abstract     = {{Abstract<br/><br>
<br/><br>
This thesis consists of the following three papers<br/><br>
<br/><br>
Paper I. Hankel operators on Bergman spaces and similarity to contractions.<br/><br>
<br/><br>
In this paper we consider Foguel-Hankel operators on vector-valued Bergman spaces. Such operators defined on Hardy spaces play a central role in the famous example by Pisier of a polynomially bounded operator which is not similar to a contraction. On Bergman spaces we encounter a completely different behaviour; power boundedness, polynomial boundedness and similarity to a contraction are all equivalent for this class of operators.<br/><br>
<br/><br>
Paper II. Weak product decompositions and Hankel operators on vector-valued Bergman spaces.<br/><br>
<br/><br>
We obtain weak product decomposition theorems, which represent the Bergman space analogues to Sarason's theorem for operator-valued Hardy spaces, respectively, to the Ferguson-Lacey theorem for Hardy spaces on product domains. We also characterize the compact Hankel operators on vector-valued Bergman spaces.<br/><br>
<br/><br>
Paper III. Discretizations of integral operators and atomic decompositions in vector-valued Bergman spaces.<br/><br>
<br/><br>
We prove a general atomic decomposition theorem for weighted vector-valued Bergman spaces, which has applications to duality problems and to the study of compact Toeplitz type operator}},
  author       = {{Constantin, Olivia}},
  isbn         = {{91-628-6625-7}},
  issn         = {{1404-0034}},
  keywords     = {{Mathematics; Matematik; Hankel operators; similarity to contractions; atomic decompositions}},
  language     = {{eng}},
  publisher    = {{KFS AB}},
  school       = {{Lund University}},
  series       = {{Doctoral Theses in Mathematical Sciences}},
  title        = {{Hankel operators and atomic decompositions in vector-valued Bergman spaces}},
  volume       = {{2005:9}},
  year         = {{2005}},
}