  This paper is essentially derived from the observation that some results used
for improving constants in the Lieb-Thirring inequalities for Schrodinger
operators in L2(-\infty,\infty) can be translated to the discrete Schrodinger
op- erators and more generally to Jacobi matrices. Some results were previ-
ously proved by D. Hundertmark and B. Simon and the aim of this article is to
improve the constants obtained in their article [7].
