Abstract :
Given a semi-group U(t) of bounded linear operators with bounded self-adjoint generator A we
estimate the logarithm of the section determinants of U(t) in terms of A. When A is subject to an
additional condition, which is related to so-called Følner sequences of orthogonal projections, this
estimate implies a Szeg˝o type theorem for bounded, self-adjoint, and strictly positive operators. We
show that the condition mentioned is satisfied when A is a Toeplitz operator or a compact operator.
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