Abstract: Nest Representations and Dynamical Systems 

Appeared: Journal of Functional Analysis, Vol 114, No. 2, June 1993.

A nest representation  is a generalized irreducible representation of a Banach
algebra on Hilbert 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
imply orbit/order conjugacy of the underlying dynamical systems. Nest algebras
and a non-free action are also considered.

Michael P. Lamoureux
University of Calgary