weakly pre-compact

Definition

• A subset S of a Banach space B is weakly pre-compact if and only if for every Banach space X and
  every Dunford-Pettis operator T: B → X, T(S) is a relatively compact subset of S.

Reference

• Rosenthal, Haskell P., Point-wise compact subsets of the first Baire class., Am. J. Math. 99, 362-378 (1977).