MEASURE OF NONCOMPACTNESS OF OPERATORS AND MATRICES ON THE SPACES c AND c0

In this note, using the Hausdorff measure of noncompactness, necessary and sufficient conditions are formulated for a linear operator and matrices between the spaces c and c0 to be compact. Among other things, some results of Cohen and Dunford are recovered. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved. We will write s, c, and c0, for the set of all complex, convergent, and null sequences, re-spectively. LetA = (anm)n,m≥1 be an infinitematrix and consider the sequence x = (xn)n≥1. We will define the produc