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 $L_{\varphi}(\widetilde{\mathcal{M}},\tau)$, where $\widetilde{\mathcal{M}}$ is a von Neumann algebra, and $\varphi$ is an Orlicz function. We show that if $\varphi\in\Delta_{2}$, $L_{\varphi}(\widetilde{\mathcal{M}},\tau)$ has the Kadec-Klee property in measure. As a corollary, the dual space and reflexivity of $L_{\varphi}(\widetilde{\mathcal{M}},\tau)$ are given.