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

2006-09-19

arxiv.org/abs/math/0609533v1

Mathematics

Operator Algebras

17 pages

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 $fU = Uf\circ \phi$. 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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