Regularized Determinants of Higher Order

In Chapter II we introduced the determinant as an extension of the determinant on the algebra of operators of finite rank; the present chapter enlarges these investigations to regularized determinants of higher order. Here these higher order determinants are studied as extensions of the corresponding regularized determinants of operators of finite rank The main extension theorem is proved in Section1, analyticity of the determinant in Section 2. In Sections 3, 4 we prove a theorem (stated in Section IV.10) which is a generalization of the Lidskii trace theorem to polynomial operator pencils.