A note on Fredholm operators on (c0)T

Characterization of some classes of compact operators between certain matrix domains of triangles

“…In this way we extend existing results. Our results are complementary to those in [2] and some of them are generalization for those in [3].…”

“…In [2], the authors considered the space (c 0 ) T = {x ∈ ω : Tx ∈ c 0 }, generalized some results on matrix transformations and compact operators on (c 0 ) T , and finally gave a sufficient condition for a linear operator on (c 0 ) T defined by an infinite matrix to be a Fredholm operator.…”

“…As in [2] and [3], this will be achieved in three steps. First we will characterize the classes (c T , cT) and (( 1 ) T , ( 1 )T), then establish identities or inequalities for the Hausdorff measure of noncompactness of the corresponding matrix operators, and give necessary and sufficient conditions for these operators to be compact, and finally, establish sufficient conditions for an infinite matrix to be a Fredholm operator on c T and ( 1 ) T .…”