An Infinite Dimensional Version of the Kostant Convexity Theorem

In this paper we generalize the linear Kostant Convexity Theorem to Lie algebras of bounded linear operators on a Hilbert space: If t is a Cartan subspace of one of the hermitian real forms h(H), ho(Ic), hsp(Ia), pt is the projection on t, U the corresponding unitary group and W the corresponding Weyl group, then for every X∈t we havept(U.X)=conv(W.X).