Isomorphisms between topological conjugacy algebras
| dc.creator | Davidson, Kenneth R. | |
| dc.creator | Katsoulis, Elias G. | |
| dc.date | 2006-02-08 | |
| dc.date | 2008-03-21 | |
| dc.date.accessioned | 2026-07-07T12:39:34Z | |
| dc.date.available | 2026-07-07T12:39:34Z | |
| dc.description | A family of algebras, which we call topological conjugacy algebras, is associated with each proper continuous map on a locally compact Hausdorff space. Assume that $η_i:\X_i\to \X_i$ is a continuous proper map on a locally compact Hausdorff space $\X_i$, for $i = 1,2$. We show that the dynamical systems $(\X_1, η_1)$ and $(\X_2, η_2)$ are conjugate if and only if some topological conjugacy algebra of $(\X_1, η_1)$ is isomorphic as an algebra to some topological conjugacy algebra of $(\X_2, η_2)$. This implies as a corollary the complete classification of the semicrossed products $C_0(\X) \times_η \bbZ^{+}$, which was previously considered by Arveson and Josephson, Peters, Hadwin and Hoover and Power. We also obtain a complete classification of all semicrossed products of the form $A(\bbD) \times_η\bbZ^{+}$, where $A(\bbD)$ denotes the disc algebra and $η: \bbD \to \bbD$ a continuous map which is analytic on the interior. In this case, a surprising dichotomy appears in the classification scheme, which depends on the fixed point set of $η$. We also classify more general semicrossed products of uniform algebras. | |
| dc.description | 25 pages. Accepted for publication in Crelle's Journal | |
| dc.identifier | https://arxiv.org/abs/math/0602172 | |
| dc.identifier | http://arxiv.org/abs/math/0602172 | |
| dc.identifier | J. reine angew. Math 621 (2008), 29-51 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/219153 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 47L80 | |
| dc.title | Isomorphisms between topological conjugacy algebras | |
| dc.type | text |