N^p Spaces

TL;DR

This paper introduces a new $N^{p}$-norm on operator spaces, establishing fundamental properties and demonstrating that the space becomes a Banach space when $W$ is complete, for all $1 \\leq p < \infty$.

Contribution

The paper defines a novel $N^{p}$-norm on operator spaces and proves that the associated space is Banach when the target space is complete.

Findings

$N^{p}$-norm is well-defined and fundamental properties are established.

The space $N^{p}(V,W)$ is Banach if $W$ is complete.

The work extends the theory of operator spaces with a new norm.

Abstract

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 $1\leq{p}<\infty$.