This is an announcement for the paper “Closed subspaces and some basic topological properties of noncommutative Orlicz spaces” by Lining Jiang, Zhenhua Ma.

Abstract: In this paper, we study the noncommutative Orlicz space Lφ(˜,τ), which generalizes the concept of noncommutative Lp space, where  is a von Neumann algebra, and φ is an Orlicz function. As a modular space, the space Lφ(˜,τ) possesses the Fatou property, and consequently, it is a Banach space. In addition, a new description of the subspace Eφ(˜,τ)=⋂Lφ(˜,τ)⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ in Lφ(˜,τ), which is closed under the norm topology and dense under the measure topology, is given. Moreover, if the Orlicz function φ satisfies the Δ2-condition, then Lφ(˜,τ) is uniformly monotone, and the convergence in the norm topology and measure topology coincide on the unit sphere. Hence, Eφ(˜,τ)=Lφ(˜,τ) if φ satisfies the Δ2-condition.

The paper may be downloaded from the archive by web browser from URL

http://arxiv.org/abs/1601.02941

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