J. Korean Math. Soc. 2011; 48(5): 1043-1052
Printed September 1, 2011
https://doi.org/10.4134/JKMS.2011.48.5.1043
Copyright © The Korean Mathematical Society.
Yun-Su Kim
The University of Toledo
We introduce a new norm, called the $N^{p}$-norm $(1 \leq p < \infty)$ on the 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 discover that if $W$ is complete, then the space $N^{p}(V,W)$ is also a Banach space with respect to this norm for $1 \leq p < \infty$.
Keywords: completely bounded maps, $N^{p}$-spaces, $N^{p}$-norm, operator spaces
MSC numbers: 46A32, 46Bxx, 46B25, 46B28, 46L07, 47L25
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