A Strong Szego Theorem for Jacobi Matrices

We use a classical result of Gollinski and Ibragimov to prove an analog of the strong Szego theorem for Jacobi matrices on $l^2(\mathbb{N})$. In particular, we consider the class of Jacobi matrices with conditionally summable parameter sequences and find necessary and sufficient conditions on the spectral measure such that ${\sum }_{k=n}^{\mathrm{\infty }}{b}_k$ and ${\sum }_{k=n}^{\mathrm{\infty }}(a_k^2-1)$ lie in $l_1^2$, the linearly-weighted $l^2$ space.