Abstract
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 $ \frac{1}{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.
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