Hankel operators and atomic decompositions in vector-valued Bergman spaces
(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:
https://lup.lub.lu.se/record/545435
- author
- Constantin, Olivia LU
- supervisor
- opponent
-
- Professor Pott, Sandra, University of Glasgow
- organization
- publishing date
- 2005
- 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
- 2019-05-21 13:33:18
@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}}, }