Dilating covariant representations of the non-commutative disc algebras

Details Dilating covariant representations of the non-commutative disc algebras Dilating covariant representations of the non-commutative disc algebras

2009-04-19

arxiv.org/abs/0904.2877v1

Mathematics

Operator Algebras

18 pages

Scientific paper

Let $\phi$ be an isometric automorphism of the non-commutative disc algebra
$\fA_n$ for $n \geq 2$. We show that every contractive covariant representation
of $(\fA_n, \phi)$ dilates to a unitary covariant representation of $(\O_n,
\phi)$. Hence the C*-envelope of the semicrossed product $\fA_n \times_{\phi}
\bZ^+$ is $\O_n \times_{\phi} \bZ$.

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