The Blum-Hanson Property

The Blum-Hanson Property

Van Oosterhout, J.M.

Haase, M.H.A. (mentor)
De Pagter, B. (mentor)

Electrical Engineering, Mathematics and Computer Science

Functional Analysis

2009-11-03

The Blum-Hanson property was identified in the 1960's as a property closely related to that of strong mixing. This property is interesting in the field of ergodic theory. It can be shown that if the orbits of all points have the Blum-Hanson property, then the operator is strongly mixing. The converse is not always true and much research has been devoted to determining when the Blum-Hanson property and the strong mixing property are in fact equivalent. After a brief introduction to ergodic theory, Chapter 2 covers all the background and definitions needed to understand the later chapters. Chapter 3 covers the major positive results to date regarding the Blum-Hanson property. Chapter 4 introduces a new class of operators that are interesting for the results in the final chapter, the Generalised Shift Operators. Results for this new class of operators are then used to analyse a number of existing examples in Chapter 5. Here existing results are extended to cover more spaces and a new counter-example is introduced based on a suggestion by László Zsidó.

Blum-Hanson property
strong mixing
ergodic theory
power-bounded
polynomially bounded

http://resolver.tudelft.nl/uuid:5d708bb4-ab43-45dc-b1e6-cee80c29143e

Student theses

master thesis

(c) 2010 Van Oosterhout, J.M.