  We provide a new proof of Volberg's Theorem characterizing thin interpolating
sequences as those for which the Gram matrix associated to the normalized
reproducing kernels is a compact perturbation of the identity. In the same
paper, Volberg characterized sequences for which the Gram matrix is a compact
perturbation of a unitary as well as those for which the Gram matrix is a
Schatten-$2$ class perturbation of a unitary operator. We extend this
characterization from $2$ to $p$, where $2 \le p \le \infty$.
