Summation of bounded sequences by regular positive matrices

In terms of elements of regular positive discrete and semicontinuous matrices sufficient conditions are obtained that these matrices do not sum a given real,divergent, bounded sequence and, in particular, that the core of a given sequence coincides with the core of the sequence (function) transformed with the aid of a matrix. These conditions permit certain facts, some well-known and some new, on the theory of inefficient matrices to be obtained.