  Using the Magri method one defines an involutive family of Hamiltonians on
Banach Lie-Poisson space iR+UL_res^1 (which contains the restricted
Grassmannian as a symplectic leaf) and on its complexification C+L_res^1. The
hierarchy of Hamilton equations given by these Hamiltonians is investigated.
The operator equations of Ricatti-type are included in this hierarchy. For a
few particular cases one gives the explicit solutions.
