Continuous derivations on algebras of locally measurable operators are inner
Continuous derivations on algebras of locally measurable operators are inner
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DOI：
10.1112/plms/pdt070
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发表时间：
2013-02
影响因子：
1.8
通讯作者：
A. Ber;V. Chilin;F. Sukochev
中科院分区：
文献类型：
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作者：
A. Ber;V. Chilin;F. Sukochev
我们证明了凡属于von Neumann代数M的所有局部可测算子的作用在 *-代数LS（M）上的每个导子必是内导子，只要它关于局部测度拓扑是连续的.特别地，LS（M）上的每个导子都是内导子，只要M是真无限vonNeumann代数。此外，任何在任意冯诺依曼代数M上的导子，其值在局部可测算子的Banach M-双模中，都是内导子。
We prove that every derivation acting on the * ‐algebra LS(M) of all locally measurable operators affiliated with a von Neumann algebra M is necessarily inner provided that it is continuous with respect to the local measure topology. In particular, every derivation on LS(M) is inner provided that M is a properly infinite von Neumann algebra. Furthermore, any derivation on an arbitrary von Neumann algebra M with values in a Banach M ‐bimodule of locally measurable operators is inner.