/ 0 30 10 07 v 1 8 J an 2 00 3 Some considerations on topologies of infinite dimensional unitary coadjoint orbits

The topology of the embedding of coadjoint orbits of the unitary group U(H) of an infinite dimensional complex Hilbert space H, as canonically determined subsets of the Banach space Ts of symmetric trace class operators, is investigated. The space Ts is identified with the B-space predual of the Lie-algebra L(H) s of the Lie group U(H). It is proved, that orbits consisting of symmetric operators with finite range are (regularly embedded) closed submanifolds of Ts.