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We study the spaces w0p, wp, and w∞p of sequences that are strongly summable to 0, summable, and bounded with index p≥1 by the Cesàro method of order 1 and establish the representations of the general bounded linear operators from the spaces wp into the spaces w∞1, w1, and w01. 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 w0p and wp into w01 and w1.

Measure of Noncompactness for Compact Matrix Operators on Some BK Spaces