An abstract Szegő theorem. (Q1419770)

The main result in this paper is an estimate of the logarithm of the section determinants for a semigroup of bounded linear operators on a complex Hilbert space, with bounded self-adjoint generator \(A\). Using the obtained estimate, the author gives a Szegö type result for bounded self-adjoint and strictly positive operators \(U\) under some condition on the operator \(A= \ln U\). The main classes of operators \(A\) satisfying this condition on \(A\) are the class of compact operators and the class of Toeplitz operators.