Strong and A-statistical comparisons for sequences

Let T and A be two nonnegative regular summability matrices and W(T,p) ∩ l∞ and cA(b) denote the spaces of all bounded strongly T -summable sequences with index p >0, and bounded summability domain of A, respectively. In this paper we show, among other things, that χN is a multiplier from W(T,p) ∩ l∞ into cA(b) if and only if any subset K of positive integers that has T -density zero implies that K has A-density zero. These results are used to characterize the A-statistical comparisons for both bounded as well as arbitrary sequences. Using the concept of A-statistical Tauberian rate, we also show that χN is not a multiplier from W(T,p) ∩ l∞ into cA(b) that leads to a Steinhaus type result.  2003 Elsevier Science (USA). All rights reserved