Compactness and collective compactness in spaces of compact operators

Abstract This is a study of compactness in (a) spaces K b ( X , Y ) of compact linear operators, (b) injective tensor products X \ bo ϵ Y , and (c) spaces L c ( X , Y ) of continuous linear operators, and its various relationships with equicontinuity and collective compactness. Among the applications is a result on factoring compact sets of compact operators compactly and uniformly through one and the same reflexive Banach space.