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- W1609889718 abstract "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^*): uin 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)." @default.
- W1609889718 created "2016-06-24" @default.
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- W1609889718 date "1999-11-17" @default.
- W1609889718 modified "2023-09-27" @default.
- W1609889718 title "Homotopy of state orbits" @default.
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