Crossed Product Structures Associated with Topological Dynamical Systems
(2009) In Doctoral Theses in Mathematical Sciences 2009:1. 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... (More)  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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1304182
 author
 Svensson, Christian ^{LU}
 supervisor

 Sergei Silvestrov ^{LU}
 opponent

 Professor Eilers, Soren, Department of Mathematical Sciences, University of Copenhagen, Denmark
 organization
 publishing date
 2009
 type
 Thesis
 publication status
 published
 subject
 keywords
 maximal abelian subalgebra, commutant, C*algebra, dynamical system, ideal, Banach algebra, Crossed product
 in
 Doctoral Theses in Mathematical Sciences
 volume
 2009:1
 pages
 109 pages
 publisher
 Centre for Mathematical Sciences, Lund University
 defense location
 Lecture Hall MH:C, Centre for Mathematical Sciences, SÃ¶lvegatan 18, Lund university, Faculty of Engineering
 defense date
 20090401 13:15:00
 ISSN
 14040034
 ISBN
 9789162877095
 project
 Noncommutative Analysis of Dynamics, Fractals and Wavelets
 language
 English
 LU publication?
 yes
 id
 85cd5ba166b84c4e8c18c69ca6a4a0fe (old id 1304182)
 date added to LUP
 20160401 13:36:51
 date last changed
 20190521 13:39:28
@phdthesis{85cd5ba166b84c4e8c18c69ca6a4a0fe, 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.<br/><br> 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 <br/><br> 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 <br/><br> C*algebras, but also prove a theorem whose counterpart in the <br/><br> C*algebra case is false. Furthermore we study the interplay between crossed products of Banach algebras by the integers and naturally associated systems.}}, author = {{Svensson, Christian}}, isbn = {{9789162877095}}, issn = {{14040034}}, keywords = {{maximal abelian subalgebra; commutant; C*algebra; dynamical system; ideal; Banach algebra; Crossed product}}, language = {{eng}}, publisher = {{Centre for Mathematical Sciences, Lund University}}, school = {{Lund University}}, series = {{Doctoral Theses in Mathematical Sciences}}, title = {{Crossed Product Structures Associated with Topological Dynamical Systems}}, volume = {{2009:1}}, year = {{2009}}, }