  We introduce a new norm, called $N^{p}$-norm $(1\leq{p}<\infty)$ on a space
$N^{p}(V,W)$ where $V$ and $W$ are abstract operator spaces. By proving some
fundamental properties of the space $N^{p}(V,W)$, we also obtain that if $W$ is
complete, then the space $N^{p}(V,W)$ is also a Banach space with respect to
this norm for $1\leq{p}<\infty$.
