Abstract. We study those orbits of oblique projections under the action of the full unitary group of a Hilbert space ${\cal H}$, which are submanifolds of ${\cal B}({\cal H})$. We also consider orbits under the Schatten unitaries, and obtain a partial characterization of the submanifold condition for these orbits. Finsler metrics are introduced, and the minimality of metric geodesics is investigated.
AMS Subject Classification
(1991): 22E65, 58E50, 58B20
Keyword(s):
oblique projections,
unitary orbits
Received June 23, 2009, and in revised form November 20, 2009. (Registered under 82/2009.)
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