Homotopy of state orbits
| dc.creator | Andruchow, E. | |
| dc.creator | Varela, A. | |
| dc.date | 1999-11-17 | |
| dc.date.accessioned | 2026-07-07T05:31:39Z | |
| dc.date.available | 2026-07-07T05:31:39Z | |
| dc.description | Let M be a von Neumann algebra, f a faithful normal state and denote by M^f the fixed point algebra of the modular group of f. Let U_M and U_{M^f} be the unitary groups of M and M^f. In this paper we study the quotient U_M/U_{M^f} endowed with two natural topologies: the one induced by the usual norm of M (called here usual topology), and the one induced by the pre-Hilbert C*-module norm given by the f-invariant conditional expectation E_f:M \to M^f (called the modular topology). It is shown that U_M/U_{M^f} is simply connected with the usual topology. Both topologies are compared, and it is shown that they coincide if and only if the Jones index of E_f is finite. The set U_M/U_{M^f} can be regarded as a model for the unitary orbit {f \circ Ad(u^*): u\in U_M} of f, and either with the usual or the modular it can be embedded continuously in the conjugate space M* (although not as a topological submanifold). | |
| dc.description | 12 pages, Latex | |
| dc.identifier | https://arxiv.org/abs/math/9911124 | |
| dc.identifier | http://arxiv.org/abs/math/9911124 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79422 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L30, 58B05 | |
| dc.title | Homotopy of state orbits | |
| dc.type | text |