Asymptotic Formulas for the Sum of Eigenvalues of Higher Order Differential Operator on Banach Space

Abstract

In this paper, we derive trace formulas for self adjoint fourth order differential operator with bounded operator coefficient in the separable Banach space. Compared with the regularized trace problems studied in Hilbert space, the fact that the asymptotic formulas obtained are on Banach space is an important result of the theoretical setting which we considered.