On Multiplicative Properties of Determinants

Abstract

Let $A$ be an elliptic pseudodifferential operator of positive order on a compact closed manifold, and let $T$ be a pseudodifferential operator of negative order such that $T^m$ is of trace class. We compute $\log \det (A(I+T))-\log \det A-\log {\det }_m(I+T)$ where first two determinants are zeta function regularized, and the last one is a regularized Fredholm determinant.

6 pages