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 FoguelHankel operators on vectorvalued 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 vectorvalued Bergman spaces.
We obtain weak product decomposition theorems, which represent the Bergman space analogues to Sarason's theorem for operatorvalued Hardy spaces, respectively, to the FergusonLacey theorem for Hardy spaces on product domains. We also characterize the compact Hankel operators on vectorvalued Bergman spaces.
Paper III. Discretizations of integral operators and atomic decompositions in vectorvalued Bergman spaces.
We prove a general atomic decomposition theorem for weighted vectorvalued Bergman spaces, which has applications to duality problems and to the study of compact Toeplitz type operator
This thesis consists of the following three papers
Paper I. Hankel operators on Bergman spaces and similarity to contractions.
In this paper we consider FoguelHankel operators on vectorvalued 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 vectorvalued Bergman spaces.
We obtain weak product decomposition theorems, which represent the Bergman space analogues to Sarason's theorem for operatorvalued Hardy spaces, respectively, to the FergusonLacey theorem for Hardy spaces on product domains. We also characterize the compact Hankel operators on vectorvalued Bergman spaces.
Paper III. Discretizations of integral operators and atomic decompositions in vectorvalued Bergman spaces.
We prove a general atomic decomposition theorem for weighted vectorvalued Bergman spaces, which has applications to duality problems and to the study of compact Toeplitz type operator
Original language  English 

Qualification  Doctor 
Awarding Institution 

Supervisors/Advisors 

Award date  2005 Oct 14 
Publisher  
ISBN (Print)  9162866257 
Publication status  Published  2005 
Bibliographical note
Defence detailsDate: 20051014
Time: 10:15
Place: Sölvegatan 18, Sal MH:C
External reviewer(s)
Name: Pott, Sandra
Title: Professor
Affiliation: University of Glasgow

Subject classification (UKÄ)
 Mathematics
Free keywords
 Mathematics
 Matematik
 Hankel operators
 similarity to contractions
 atomic decompositions