Finite families of $l_p$-spaces and multirectangular characteristics

Under consideration are finite families of Banach spaces with unconditional basis. The problem of isomorphic classification of families is studied together with the related problem of uniqueness of an unconditional basis for a family. Complete solution of both problems for $l_1$- and $c_0$-families is given by using some geometric invariants combined with the corresponding results for $l_1$ and $c_0$.