Topics on the Degenerate Elliptic Differential Operators far From Self Adjoint Ones

Background: Elliptic differential operators and asymptotic distribution of eigenvalues of them are discussed in many works.Methods: In this paper we get some new results about an important differential operator on a Hilbert space. Also asymptotic distribution of eigenvalues of this kind of differential operators are proved with new methods that estimation of the resolvent of the operators is used in this paper.Finding: We get some new theorems about the differential operator A. We consider a bounded domain    with smooth boundary in  define a norm and find the asymptotic distribution of eigenvalues of the operator in the space .Improvement: we improve the method of proving this kind of theorems.