Nest Representations and Dynamical Systems

A nest representation is a generalized irreducible representation of a Banach algebra on Hubert space. For a free, discrete dynamical system, every ideal in the semicrossed product algebra is equal to an intersection of kernels of nest representations; a proper subset of all such kernels is a topological space homeomorphic to the space of all (discrete) finite arcs in the dynamical system, with the subarc topology. For certain continuous dynamical systems, the corresponding set of kernels is isomorphic to the topological space of (continuous) finite arcs. A Banach algebra isomorphism of semicrossed products implies orbit/order conjugacy of the underlying dynamical systems. Nest algebras and a non-free action are also considered.