Kadec-Klee property for convergence in measure of noncommutative Orlicz spaces

Abstract

In this paper, we study the Kadec-Klee property for convergence in measure of noncommutative Orlicz spaces $L_{\phi }(\tilde{\mathcal{M}},\tau )$, where $\tilde{\mathcal{M}}$ is a von Neumann algebra, and $\phi$ is an Orlicz function. We show that if $\phi \in {\Delta }_2$, $L_{\phi }(\tilde{\mathcal{M}},\tau )$ has the Kadec-Klee property in measure. As a corollary, the dual space and reflexivity of $L_{\phi }(\tilde{\mathcal{M}},\tau )$ are given.

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