TWO METHODS FOR THE CHARACTERIZATION OF COMPACT OPERATORS BETWEEN BK SPACES

We establish some identities or inequalities for the Hausdorff measure of noncompactness for operators L is an element of B( X, Y) when X = l(p) (1 <= p < infinity) and Y = c; X = l(p) (1 < p < infinity) and Y = l(infinity); X = bv(0) and Y = c; X = c(0)(Delta), c(Delta), l(infinity) (Delta) and Y = l(infinity). These identities and estimates are used to establish necessary and sufficient conditions for the operators to be compact. Furthermore, we apply a result by Sargent to establish necessary and sufficient conditions for operators in B(bv(0), l(infinity)) and B(l(1), Y) to be compact, where Y = w(infinity), v(infinity), [c](infinity).