The Jacobson Radical for Analytic Crossed Products

The Jacobson Radical for Analytic Crossed Products

We characterise the Jacobson radical of an analytic crossed product C0(X)×φZ+, answering a question first raised by Arveson and Josephson in 1969. In fact, we characterise the Jacobson radical of analytic crossed products C0(X)×φZd+. This consists of all elements whose “Fourier coefficients” vanish...

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Veröffentlicht in:Journal of functional analysis 2001-12, Vol.187 (1), p.129-145
Hauptverfasser: Donsig, Allan P, Katavolos, Aristides, Manoussos, Antonios
Format: Artikel
Sprache:eng
Schlagworte:
analytic crossed products
Jacobson radical
recurrence
semicrossed products
wandering sets
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Zusammenfassung:We characterise the Jacobson radical of an analytic crossed product C0(X)×φZ+, answering a question first raised by Arveson and Josephson in 1969. In fact, we characterise the Jacobson radical of analytic crossed products C0(X)×φZd+. This consists of all elements whose “Fourier coefficients” vanish on the recurrent points of the dynamical system (and the first one is zero). The multidimensional version requires a variation of the notion of recurrence, taking into account the various degrees of freedom.
ISSN:0022-1236
1096-0783
DOI:10.1006/jfan.2001.3819