  We prove Lieb-Thirring-type bounds on eigenvalues of non-selfadjoint Jacobi
operators, which are nearly as strong as those proven previously for the case
of selfadjoint operators by Hundertmark and Simon. We use a method based on
determinants of operators and on complex function theory, extending and
sharpening earlier work of Borichev, Golinskii and Kupin.
