Let ℳ be a semifinite von Neumann algebra with a faithful semifinite normal trace τ. Assume that E(0, ∞) is an M-embedded fully symmetric function space having order continuous norm and is not a superset of the set of all bounded vanishing functions on (0, ∞). In this paper, we prove that the corresponding operator space E(ℳ, τ) is also M-embedded. It extends earlier results by Werner [48, Proposition 4∙1] from the particular case of symmetric ideals of bounded operators on a separable Hilbert space to the case of symmetric spaces (consisting of possibly unbounded operators) on an arbitrary semifinite von Neumann algebra. Several applications are given, e.g., the derivation problem for noncommutative Lorentz spaces ℒp,1(ℳ, τ), 1 < p < ∞, has a positive answer.

中文翻译：

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M-embedded 对称算子空间和推导问题

令 ℳ 为具有忠实半有限正态迹的半有限冯诺依曼代数τ. 假使，假设乙(0, ∞) 是一个米- 具有顺序连续范数的嵌入完全对称函数空间，并且不是 (0, ∞) 上所有有界消失函数的集合的超集。在本文中，我们证明了相应的算子空间乙(ℳ, τ) 也是米-嵌入式。它将 Werner [48, Proposition 4∙1] 的早期结果从可分离希尔伯特空间上的有界算子的对称理想的特殊情况扩展到任意半有限冯诺依曼代数上的对称空间（可能由无界算子组成）的情况。给出了几个应用，例如，非交换洛伦兹空间的推导问题ℒp,1(ℳ, τ), 1 < p < ∞, 有一个肯定的答案。