Ideal metrics in the problem of approximating the distributions of sums of independent random variables

In two previous publications [5] and [6], the author introduced special metrics in spaces of probability measures in Banach spaces $U$. These metrics, called ideal, were used in studying approximations of the distributions of sums of independent $U$-valued random variables.
In this paper, a number of new general properties of ideal metrics are established and the possibility of using them in the above problems is demonstrated. In particular, a generalization and refinement of a recent result due to V. Paulauskas is given.