Biholomorphisms of the unit ball of \(\mathbb C^n\) and semicrossed products. (English) Zbl 1222.47133
Bercovici, Hari (ed.) et al., Operator theory live. Proceedings of the 22nd international conference on operator theory, Timişoara, Romania, July 3–8, 2008. Bucharest: The Theta Foundation (ISBN 978-973-87899-6-8). Theta Series in Advanced Mathematics 12, 69-80 (2010).
Summary: Assume that \(\phi_1\) and \(\phi_2\) are automorphisms of the non-commutative disc algebra \({\mathfrak A}_n\), \(n\geq 2\). We show that the semicrossed products \({\mathfrak A}_n\times_{\phi_1}\mathbb{Z}^+\) and \({\mathfrak A}_n\times_{\phi_2} \mathbb{Z}^+\) are isomorphic as algebras if and only if \(\phi_1\) and \(\phi_2\) are conjugate via an automorphism of \({\mathfrak A}_n\). A similar result holds for semicrossed products of the \(d\)-shift algebra \({\mathcal A}_d\), \(d\geq 2\).
For the entire collection see [Zbl 1200.46002].
For the entire collection see [Zbl 1200.46002].
MSC:
| 47L55 | Representations of (nonselfadjoint) operator algebras |
| 47L40 | Limit algebras, subalgebras of \(C^*\)-algebras |
| 46L05 | General theory of \(C^*\)-algebras |
| 37B20 | Notions of recurrence and recurrent behavior in topological dynamical systems |
| 37B99 | Topological dynamics |
