Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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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.

$N^{p}$-spaces

Yun-Su Kim

The University of Toledo

Abstract

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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