The Jacobson radical for analytic crossed products

Abstract

We characterise the (Jacobson) radical of the analytic crossed product of C_0(X) by the non-negative integers (Z_+), answering a question first raised by Arveson and Josephson in 1969. In fact, we characterise the radical of analytic crossed products of C_0(X) by (Z_+)^d. The radical 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.

17 pages; AMS-LaTeX; minor corrections

Cited by in corpus (7)

• The C${}^{\ast }$-envelope of a semicrossed product and nest representations
• Semicrossed products of C*-algebras and their C*-envelopes
• Semicrossed products of the disk algebra and the Jacobson radical
• On the Primitive Ideals of Nest Algebras
• Piecewise conjugacy for multivariable dynamics over the Jacobson spectrum of a C*-algebra
• Isomorphisms between topological conjugacy algebras
• Operator algebras for multivariable dynamics