Compact operators whose adjoints factor through subspaces of lp

For p≥ 1, a subset K of a Banach space X is said to be relatively p-compact if K ⊂ \ ∑ ₙ₌₁^∞ αₙ xₙ : \αₙ\ ∈ Ball (lp') \, where p'=p/(p-1) and $\{x_n\}∈ l_pˢ