The Second Regularized Trace of Even Order Differential Operators with Operator Coefficient

Abstract

In this paper, we investigate the spectrum of the self adjoint operator L defined by
L := (-1)^r+ d^2r/dx^2r + A + Q(x),
where A is a self adjoint operator, Q(x) is a nuclear operator in a separable Hilbert space, and we derive asymptotic formulas for the sum of eigenvalues of the operator L.