<Abstract>The results of invertibility and spectrum for some different classes of infinite-dimensional Hamiltonian operators,after a brief classification by domains,are given.By the above results,the associated infinite-dimensional Hamiltonian operator with simple supported rectangular plate is proved to be invertible.Furthermore,by a certain compactness,we find that the spectrum of this operator consists only of isolated eigenvalues with finite geometric multiplicity,which will play a significant role in finding the analytical and numerical solution based on Hamiltonian system for a class of plate bending equations.
