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

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

2008-10-29

arxiv.org/abs/0810.5364v1

Mathematics

Operator Algebras

Scientific paper

Let $X$ be compact Hausdorff, and $\phi: X \to X$ a continuous surjection. Let $\mathcal{A}$ be the semicrossed product algebra corresponding to the relation fU = Uf\circ \phi$ or to the relation $Uf = f\circ \phi U.$ Then the C$^*$-envelope of $\mathcal{A}$ is the crossed product of a commutative C$^*$-algebra which contains $C(X)$ as a subalgebra, with respect to a homeomorphism which we construct. We also show there are"sufficiently many" nest representations.

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