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arXiv · 1610.03948

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

Zhenhua Ma·Lining Jiang·Kai Ji
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Abstract

In this paper, we study the Kadec-Klee property for convergence in measure of noncommutative Orlicz spaces $L_φ(\widetilde{\mathcal{M}},τ)$, where $\widetilde{\mathcal{M}}$ is a von Neumann algebra, and $φ$ is an Orlicz function. We show that if $φ\inΔ_{2}$, $L_φ(\widetilde{\mathcal{M}},τ)$ has the Kadec-Klee property in measure. As a corollary, the dual space and reflexivity of $L_φ(\widetilde{\mathcal{M}},τ)$ are given.

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Zhenhua Ma, Lining Jiang, Kai Ji. 2016-10-13. Kadec-Klee property for convergence in measure of noncommutative Orlicz spaces. https://arxiv.org/abs/1610.03948

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