The Jacobson radical for analytic crossed products

Abstract

We characterise the Jacobson radical of an analytic crossed product C0(X) xφ ℤ+, answering a question first raised by Arveson and Josephson in 1969. In fact, we characterise the Jacobson radical of analytic crossed products C0(X) xφ 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 multidimensional version requires a variation of the notion of recurrence, taking into account the various degrees of freedom. © 2001 Academic Press.