Abstract
We study the spaces w(0)(p), w(p), and w(omega)(p) of sequences that are strongly summable to 0, summable, and bounded with index p > 1 by the Cesaro method of order 1 and establish the representations of the general bounded linear operators from the spaces w(p) into the spaces w(omega)(1), w(1), and w(0)(1). We also give estimates for the operator norm and the Hausdorff measure of noncompactness of such operators. Finally we apply our results to characterize the classes of compact bounded linear operators from w(0)(p) and w(p) into w(0)(1) and w(1).