Central limit theorem for the Banach-valued weakly dependent random variables

Let $B$ be a separable Banach space, $\xi_i$ – a stationary sequence of $B$-valued random variables with zero mean. In this paper we investigate some conditions on the character and rate of mixing under which the sequence $\xi_i$ satisfies the central limit theorem, i. e. the sequence
$$ S_n=n^{-1/2}(\xi_1+\dots+\xi_n),\qquad n\to\infty, $$
converges weakly to some Gaussian $B$-valued variable.