In this paper, we characterize the classes ((?1)T, (?1)?T ) and (cT, c?T)
where T = (tnk)?n,k=0 and ?T=(?tnk)?n,k=0 are arbitrary triangles. We
establish identities or estimates for the Hausdorff measure of noncompactness
of operators given by matrices in the classes ((?1)T, (?1)?T ) and (cT, c?T).
Furthermore we give sufficient conditions for such matrix operators to be
Fredholm operators on (?1)T and cT. 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].