On the ascent of infinite dimensional Hamiltonian operators

In this paper, the ascent of 2×2 infinite dimensional Hamiltonian operators and a class of 4×4 infinite dimensional Hamiltonian operators are studied, and the conditions under which the ascent of 2×2 infinite dimensional Hamiltonian operator is 1 and the ascent of a class of 4×4 infinite dimensional Hamiltonian operators that arises in study of elasticity is 2 are obtained. Concrete examples are given to illustrate the effectiveness of criterions.