A note on Fredholm operators on (c0)T(c0)T

We characterize the class ((c0)T,(c0)T̃) where T=(tnk)n,k=0∞ and T̃=(t̃nk)n,k=0∞ are triangles. Using the Hausdorff measure of noncompactness, we define the class of compact operators given by matrices in ((c0)T,(c0)T̃). Furthermore we give a sufficient condition for a matrix operator to be a Fredholm operator on (c0)T(c0)T.