Abstract
We study connections between topological dynamical systems and associated algebras of crossed product type. We derive equivalences between structural properties of a crossed product and dynamical properties of the associated system and furthermore derive qualitative results concerning the crossed product that are true regardless of the corresponding dynamical system. The systems principally investigated are pairs of a compact Hausdorff space and a homeomorphism, where the integers act on former via iterations of the latter.
With such a system a crossed product C*algebra can be associated. We do not only focus on the C*crossed product of a system, but also on a Banach *algebra and a noncomplete *algebra that can both be embedded by *isomorphisms as dense subalgebras of the C*algebra; the C*crossed product is the socalled enveloping
C*algebra of this Banach *algebra. While investigations of the connections between a system and its C*algebra have an extensive history, considerations of the other two algebras are new. For these algebras, we derive analogues of results from the case of
C*algebras, but also prove a theorem whose counterpart in the
C*algebra case is false. Furthermore we study the interplay between crossed products of Banach algebras by the integers and naturally associated systems.
With such a system a crossed product C*algebra can be associated. We do not only focus on the C*crossed product of a system, but also on a Banach *algebra and a noncomplete *algebra that can both be embedded by *isomorphisms as dense subalgebras of the C*algebra; the C*crossed product is the socalled enveloping
C*algebra of this Banach *algebra. While investigations of the connections between a system and its C*algebra have an extensive history, considerations of the other two algebras are new. For these algebras, we derive analogues of results from the case of
C*algebras, but also prove a theorem whose counterpart in the
C*algebra case is false. Furthermore we study the interplay between crossed products of Banach algebras by the integers and naturally associated systems.
Original language  English 

Qualification  Doctor 
Awarding Institution 

Supervisors/Advisors 

Award date  2009 Apr 1 
Publisher  
ISBN (Print)  9789162877095 
Publication status  Published  2009 
Bibliographical note
Defence detailsDate: 20090401
Time: 13:15
Place: Lecture Hall MH:C, Centre for Mathematical Sciences, Sölvegatan 18, Lund university, Faculty of Engineering
External reviewer(s)
Name: Eilers, Soren
Title: Professor
Affiliation: Department of Mathematical Sciences, University of Copenhagen, Denmark

Subject classification (UKÄ)
 Mathematics
Free keywords
 maximal abelian subalgebra
 commutant
 C*algebra
 dynamical system
 ideal
 Banach algebra
 Crossed product