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Abstract: In this paper, we consider both algebraic crossed products of commutativecomplex algebras A with the integers under an automorphism of A, and Banachalgebra crossed products of commutative C^*-algebras A with the integers underan automorphism of A. We investigate, in particular, connections betweenalgebraic properties of these crossed products and topological properties ofnaturally associated dynamical systems. For example, we draw conclusions aboutthe ideal structure of the crossed product by investigating the dynamics ofsuch a system. To begin with, we recall results in this direction in thecontext of an algebraic crossed product and give simplified proofs ofgeneralizations of some of these results. We also investigate new questions,for example about ideal intersection properties of algebras properly betweenthe coefficient algebra A and its commutant A-. Furthermore, we introduce aBanach algebra crossed product and study the relation between the structure ofthis algebra and the topological dynamics of a naturally associated system.



Autor: Christian Svensson, Sergei Silvestrov, Marcel de Jeu

Fuente: https://arxiv.org/







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