On the ascent of infinite dimensional Hamiltonian operators**Project supported by the National Natural Science Foundation of China (Grant Nos. 11101200 and 11371185) and the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2013ZD01).

Abstract

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.