THE JACOBSON RADICAL FOR ANALYTIC CROSSED PRODUCTS

Authors

Allan P. Donsig, University of Nebraska-LincolnFollow
Aristides Katavolos, University of AthensFollow
Antonios ManoussosFollow

Document Type

Article

Date of this Version

2001

Citation

Journal of Functional Analysis. 2000 Math.

Comments

Primary: 47L65; Secondary: 46H10, 46K50.

Abstract

We characterise the Jacobson radical of an analytic crossed product C₀(X) ×_Ø Z^d₊, answering a question first raised by Arveson and Josephson in 1969. In fact, we characterise the Jacobson radical of analytic crossed products C₀(X) ×_Ø Z^d₊. This consists of all elements whose ‘Fourier coefficients’ vanish on the recurrent points of the dynamical system (and the first one is zero). The multi-dimensional version requires a variation of the notion of recurrence, taking into account the various degrees of freedom.