The C$^*$-envelope of a semicrossed product and Nest Representations

Justin R. Peters

paper

The C $^{*}$ -envelope of a semicrossed product and Nest Representations

arXiv:0810.5364

Abstract

Let $X$ be compact Hausdorff, and $ϕ : X \to X$ a continuous surjection. Let $A$ be the semicrossed product algebra corresponding to the relation fU = Uf\circ ϕ $or t o t h er e l a t i o n$ Uf = f\circ ϕU. $T h e n t h e C$ ^* $- e n v e l o p eo f$ \mathcal{A} $i s t h ecr osse d p r o d u c t o f a co mm u t a t i v e C$ ^* $- a l g e b r a w hi c h co n t ain s$ C(X)$ as a subalgebra, with respect to a homeomorphism which we construct. We also show there are"sufficiently many" nest representations.

The C∗-envelope of a semicrossed product and Nest Representations

Abstract

The C $^{*}$ -envelope of a semicrossed product and Nest Representations