
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 -norm on a space where and are abstract operator spaces. By proving some fundamental properties of the space , we also obtain that if is complete, then the space is also a Banach space with respect to this norm for .
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Taxonomy
TopicsAdvanced Banach Space Theory · Holomorphic and Operator Theory · Advanced Harmonic Analysis Research
