A note on Fredholm operators on

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