Structure of derivations on various algebras of measurable operators for type I von Neumann algebras
Structure of derivations on various algebras of measurable operators for type I von Neumann algebras
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DOI：
10.1016/j.jfa.2008.11.003
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发表时间：
2008-08
影响因子：
1.7
通讯作者：
S. Albeverio;Sh. A. Ayupov;K. Kudaybergenov
中科院分区：
文献类型：
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作者：
S. Albeverio;Sh. A. Ayupov;K. Kudaybergenov
给定一个von Neumann代数M，分别用S(M)和LS(M)表示与M相关的所有可测算子和局部可测算子的代数。对于M上的可靠正规半有限迹τ，设S（M,τ）为S(M)中所有τ可测算子的代数。在I型von Neumann代数M的情况下，给出了上述算子代数上的所有导数的完整描述，特别是证明了如果M是I∞型，则LS(M)上的每一个导数（p. 1）。S（M)和S(M,τ)）是内的。
Given a von Neumann algebra M denote by S(M) and LS(M) respectively the algebras of all measurable and locally measurable operators affiliated with M. For a faithful normal semi-finite trace τ on M let S(M,τ) be the algebra of all τ-measurable operators from S(M). We give a complete description of all derivations on the above algebras of operators in the case of type I von Neumann algebra M. In particular, we prove that if M is of type I∞then every derivation on LS(M) (resp. S(M) and S(M,τ)) is inner.