  Let G be a complex semisimple Lie group and \tau a complex antilinear
involution that commutes with the Cartan involution. If H denotes the connected
subgroup of \tau-fixed points in G, and K is maximally compact, each H-orbit in
G/K can be equipped with a Poisson structure as described by Evens and Lu. We
consider symplectic leaves of certain such H-orbits with a natural hamiltonian
torus action. A symplectic convexity theorem of Hilgert-Neeb-Plank then leads
to van den Ban's convexity theorem for (complex) semisimple symmetric spaces.
