  A wide new class of subsets of a Banach space $X$ named coarse $p$-limited
sets ($ 1\leq p < \infty$) is introduced by considering weak* $p$-summable
sequences in $X'$ instead of weak* null sequences. We study its basic
properties and compare it with the class of compact and weakly compact sets.
Results concerning the relationship of coarse $p$-limited sets with operators
are obtained.
