Representation of compact operators between Banach spaces

In this article, we give a representation for compact operators acting between reflexive Banach spaces, which generalizes the representation given by Edmunds et al. for compact operators between reflexive Banach spaces with strictly convex duals. Further, we give a representation for a class of operators on Banach spaces, that is comparable to the classical spectral representation for compact normal operators on Hilbert spaces. Finally, we give an example to illustrate our main result.