N^p Spaces

We introduce a new norm, called $N^p$-norm $(1\le p<\mathrm{\infty })$ 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 $1\le p<\mathrm{\infty }$.