A generalization of Pincus' formula and Toeplitz operator determinants

In this paper we prove the following result. Let A and B be bounded linear operator on a Hilbert space such that AB - BA is trace class. Then the operator determinant of e(A)e(B)e(-A-B) is well defined and equals the exponential of 2 trace (AB - BA). This generalization of a formula due to Pincus can be applied to find explicit expressions for operator determinants that appear in the theory of Toeplitz operators.