Matrix mappings and general bounded linear operators on the space bv

Abstract

If X and Y are FK spaces, then every infinite matrix A ∈ (X, Y) defines a bounded linear operator LA ∈ B(X, Y) where LA(x) = Ax for each x ∈ X. But the converse is not always true. Indeed, if L is a general bounded linear operator from X to Y, that is, L ∈ B(X, Y), we are interested in the representation of such an operator using some infinite matrices. In this paper we establish the representations of the general bounded linear operators from the space bv into the spaces ℓ∞, c and c0. We also prove some estimates for their Hausdorff measures of noncompactness. In this way we show the difference between general bounded linear operators between some sequence spaces and the matrix operators associated with matrix transformations.