Physics – Mathematical Physics
Scientific paper
2003-01-08
Journal of Geometry and Physics 51 (2004) 256-268
Physics
Mathematical Physics
13 pages; corrected an error in formulation and proof of a lemma, and also its consequences; the proof of main assertion was s
Scientific paper
10.1016/j.geomphys.2003.10.010
The topology of the embedding of the coadjoint orbits of the unitary group U(H) of an in-finite dimensional complex Hilbert space H, as canonically determined subsets of the B-space T_s of symmetric trace class operators, is investigated. The space T_s 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 con-sisting of symmetric operators with finite range are (regularly embedded) closed submanifolds of T_s. An alternative method of proving this fact is given for the `one-dimensional' orbit, i.e. for the projective Hilbert space P(H). Also a technical assertion concerning existence of simply related decompositions into one-dimensional projections of two unitary equivalent (orthogonal) projections in their `generic mutual position' is formulated, proved, and illustrated.
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