Dilating covariant representations of the non-commutative disc algebras

Davidson, K. R.; Katsoulis, E. G.

Dilating covariant representations of the non-commutative disc algebras

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Description

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