Hamiltonian Carleman Approximation of the Calogero-Moser Space

We derive the Hamiltonian tangential Carleman approximation for the complex Calogero-Moser space Cₙ with a non-compact real form CₙR, using the symplectic density property of Cₙ. The Hamiltonian tangential Carleman approximation means to approximate symplectic diffeomorphisms of CₙR which are smoothly isotopic to the identity by symplectic holomorphic automorphisms of Cₙ which in addition preserve the real form CₙR. This appproximation is in the strongest topology, in the fine Whitney topology.