17.5.2023
Doctoral Thesis on Different Types of Weighted Composition Operators on Banach Spaces of Analytic Functions
M.Sc. David Norrbo’s doctoral thesis in Mathematics will be put forth for public defence at the Faculty of Science and Engineering at Åbo Akademi University.
The thesis is entitled Different types of weighted composition operators on Banach spaces of analytic functions.
The public defence of the doctoral thesis takes place on 26 May 2023 at 1 PM in auditorium XX, Agora, Vesilinnantie 3, Turku. Associate Professor Karl-Mikael Perfekt, NTNU: Norwegian University of Science and Technology, Norway will serve as opponent and Professor Mikael Lindström, Åbo Akademi University, as custos.
Summary
Many problems in real life are, at least approximatively, of linear nature and can be mathematically examined with the aid of linear spaces. It is natural to measure the size of objects occurring in the problems and such an operation is called a norm. If the space and the norm fit well together, they constitute a Banach space. A norm associates every vector with a nonnegative number or infinity, and the Banach space consists of those vectors whose associated number is finite. Different norms give rise to different Banach spaces.
In the thesis, which contains three articles, different types of weighted composition operators on Banach spaces, consisting of analytic functions defined on the unit disc of the complex plane, are examined. Since the vectors are functions, there are two basic linear operations to consider. One way to modify the vector is by multiplying it with another function. Such an operator is said to be a multiplication operator if it is well defined. Another way to modify the vector is to first transform the input via a function and make the original vector act on the modified input. Such a transformation is done by a composition operator. A combination of a multiplication operator and a composition operator is said to be a weighted composition operator.
In one of the articles, a certain class of integral operators on weighted Bergman spaces are examined. The exact value of the essential norm of such operators, which can be represented as a mean of weighted composition operators, is calculated. Another article deals with the connection between some operator-theoretic properties of a weighted composition operator on the Banach space BMOA and the behaviour of corresponding functions. Compactness, weak compactness and complete continuity are examined. In the so far not mentioned article, the spectrum and essential spectrum are determined for multiplication operators on some Banach spaces.
David Norrbo was born in 1993 in Nykarleby. He can be reached by email at david.norrbo@abo.fi.
The doctoral thesis can be read online through the Doria publication archive.