Characterization of Some Classes of Compact Operators between Certain Matrix Domains of Triangles

In this paper, we characterize the classes ((l(1))(T), (l(1))((T) over tilde)) and (c(T), c((T) over tilde)) where T = (t(nk))(n,k=0)(infinity) and (T) over tilde = (t(nk))(n,k=0)(infinity) are arbitrary triangles. We establish identities or estimates for the Hausdorff measure of noncompactness of operators given by matrices in the classes ((l(1))(T), (l(1))((T) over tilde)) and (c(T), c((T) over tilde)). Furthermore we give sufficient conditions for such matrix operators to be Fredholm operators on (l(1))(T) and c(T). As an application of our results, we consider the class (bv, bv) and the corresponding classes of matrix operators. Our results are complementary to those in [2] and some of them are generalization for those in [3].