Abstract :
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
