Noncommutative spectral synthesis for the involutive Banach algebra associated with a topological dynamical system

Autor:	de Jeu, Marcel, Tomiyama, Jun
Rok vydání:	2012
Předmět:	Mathematics - Functional Analysis Mathematics - Operator Algebras 46K99 (Primary) 46H10 47L65 (Secondary)
Zdroj:	Banach J. Math. Anal. 7 (2013), 103-135
Druh dokumentu:	Working Paper
DOI:	10.15352/bjma/1363784226
Popis:	If X is a compact Hausdorff space, supplied with a homeomorphism, then a crossed product involutive Banach algebra is naturally associated with these data. If X consists of one point, then this algebra is the group algebra of the integers. In this paper, we study spectral synthesis for the closed ideals of this associated algebra in two versions, one modeled after C(X), and one modeled after the group algebra of the integers. We identify the closed ideals which are equal to (what is the analogue of) the kernel of their hull, and determine when this holds for all closed ideals, i.e., when spectral synthesis holds. In both models, this is the case precisely when the homeomorphism has no periodic points. Comment: 28 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1206.0158 Zobrazit plný text záznamu View this record from Arxiv