  In this paper, we study the number of limit cycles that can bifurcating from
a periodic annulus in discontinuous planar piecewise linear Hamiltonian
differential system with three zones separated by two parallel straight lines.
We prove that if the central subsystem, i.e. the system defined between the two
parallel lines, has a real center and the others subsystems have centers or
saddles, then we have at least three limit cycles that appear after
perturbations of periodic annulus. For this, we study the number of zeros of a
Melnikov function for piecewise Hamiltonian system and present a normal form
for this system in order to simplify the computations.
