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Dynamical systems associated with crossed products
Leiden University, Netherlands .
Lund university. (Mathematics/Applied Mathematics)ORCID iD: 0000-0003-4554-6528
Leiden University, Netherlands .
2009 (English)In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, ISSN 0167-8019, E-ISSN 1572-9036, ISSN 0167-8019, Vol. 108, no 3, 547-559 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we consider both algebraic crossed products of commutative complex algebras A with the integers under an automorphism of A, and Banach algebra crossed products of commutative C*-algebras A with the integers under an automorphism of A. We investigate, in particular, connections between algebraic properties of these crossed products and topological properties of naturally associated dynamical systems. For example, we draw conclusions about the ideal structure of the crossed product by investigating the dynamics of such a system. To begin with, we recall results in this direction in the context of an algebraic crossed product and give simplified proofs of generalizations of some of these results. We also investigate new questions, for example about ideal intersection properties of algebras properly between the coefficient algebra A and its commutant A'. Furthermore, we introduce a Banach algebra crossed product and study the relation between the structure of this algebra and the topological dynamics of a naturally associated system.

Place, publisher, year, edition, pages
Springer, 2009. Vol. 108, no 3, 547-559 p.
Keyword [en]
Dynamical system, C*-algebra, Banach algebra, periodic point, aperiodic point, maximal commutative subalgebra, ideal
National Category
Mathematical Analysis Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-22076DOI: 10.1007/s10440-009-9506-5ISI: 000271941500006Scopus ID: 2-s2.0-71449105220OAI: oai:DiVA.org:mdh-22076DiVA: diva2:682603
Funder
Swedish Research Council
Available from: 2013-12-28 Created: 2013-10-23 Last updated: 2014-01-10Bibliographically approved

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Publisher's full textScopushttp://dx.doi.org/10.1007/s10440-009-9506-5

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Silvestrov, Sergei
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CiteExportLink to record
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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
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Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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Output format
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