Let $X$ be a separable Banach space and $1<p<\infty$. We say that a sequence $(x_{n})_{n}$ in $X$ is weakly $p$-convergent to $x\in X$ if the sequence $(x_{n}-x)_{n}$ is weakly $p$-summable. A subset $K$ of $X$ is said to be relatively weakly $p$-compact if $K$ is contained in $S(B_{l_{p^{*}}})$ for some operator $S$ from $l_{p^{*}}$ into $X(\frac{1}{p}+\frac{1}{p^{*}}=1)$. My question is: A subset $K$ of $X$ is relatively weakly $p$-compact if and only if every sequence in $K$ admits a weakly $p$-convergent subsequence? Thank you.