Journal of Operator Theory

Volume 56, Issue 2, Fall 2006 pp. 343-355.

Regular normed bimodules

Authors: Chi-Keung Ng
Author institution: The Chern Instit. of Mathematics and LPMC, Nankai University, Tianjin 300071, P.R. China

Summary: In this article, we will give a characterization of Banach bimodules over $C^*$-algebras of compact operators that arise from operator spaces as well as a characterization of (F)-Banach bundles amongst all (H)-Banach bundles over a hyper-Stonian space. These two characterizations are concerned with whether a certain natural map from a Banach bimodule to its canonical bidual is isometric (we call such bimodule \textit{regular}).

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