Dilating covariant representations of the non-commutative disc algebras. (English) Zbl 1202.46079
Summary: Let \(\varphi\) be an isometric automorphism of the non-commutative disc algebra \({\mathfrak A}_n\), for \(n\geq 2\). We show that every contractive covariant representation of \(({\mathcal O},\varphi)\) dilates to a unitary covariant representation of \(({\mathcal O}_n,\varphi)\). Hence the \(C^*\)-envelope of the semicrossed product \({\mathfrak A}_n\times _\varphi\mathbb Z^+\) is \({\mathcal O}_n\times_\varphi\mathbb Z\).
MSC:
| 46L55 | Noncommutative dynamical systems |
| 47A13 | Several-variable operator theory (spectral, Fredholm, etc.) |
Keywords:
non-commutative disk algebra; dilation; semicrossed product; Cuntz algebra; crossed productReferences:
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