Some theorems on matrix transforms between speed-Maddox spaces

First, in this paper, the notions of convergence and boundedness with speed, and the notion of speed-Maddox spaces are recalled. Let X, Y be two sets of sequences with real or complex entries, and (X, Y) the set of matrices (with real or complex entries) to map X into Y. Let ? and ? be speeds of the convergence, i.e.; monotonically increasing positive sequences. Necessary and sufficient conditions for a matrix A ? (X, Y), if X is the certain speed-Maddox space defined by ?, and Y is another speed-Maddox space defined by ? are proved. As an application of main results, one example where A is the Zweier matrix Z1/2 is presented.