Application to Compact Matrix Operators

Abstract

In this chapter, we present some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain operators given by infinite matrices that map an arbitrary BK space into the sequence spaces \(c_{0}\), \(c\), \(\ell _{\infty }\) and \(\ell _{1}\), and into the matrix domains of triangles in these spaces. It is shown that many linear compact operators may be represented as matrix operators in sequence spaces or integral operators in function spaces.