Some estimates of the accuracy of approximation in the multidimensional central limit theorem

The paper contains some estimates of the remainder term in the central limit theorem for the case of general Banach space and for its particular case $R_m$ ($m\le 5$). In the case of general Banach space the special metrics $\lambda_k$ are used, which are defined by means of characteristic functions. In the case of $R_m$ ($m\le 5$) we use the well-known Levy–Prohorov metrics.