A note on relative compactness in K(X,Y)

Abstract

For Banach spaces $X$ and $Y$, let $K(X,Y)$ denote the space of all compact operators from $X$ to $Y$ endowed with the operator norm. We give sufficient conditions for subsets of $K(X,Y)$ to be relatively compact. We also give some necessary and sufficient conditions for the Dunford–Pettis relatively compact property of some spaces of operators.