LINEARIZATION, TRACE, AND DETERMINANT OF CERTAIN MEROMORPHIC OPERATOR-FUNCTIONS

In this paper operator functions of type(~)[GRAPHICS](~)are considered. In the first part of the paper a linearization of L is constructed under certain convergence conditions, and it is shown that the geometric multiplicities and the null multiplicities of the eigenvalues lambda is-an-element-of C of L and the linearization coincide. In the second part of the paper trace and determinant formulas for L are derived under some further conditions for the coefficients of L.