Nest-subalgebras of von Neumann algebras
Nest-subalgebras of von Neumann algebras
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DOI：
10.1016/0001-8708(82)90022-6
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发表时间：
1982-11
影响因子：
1.7
通讯作者：
F. Gilfeather;D. Larson
中科院分区：
文献类型：
--
作者：
F. Gilfeather;D. Larson
研究了一类可分离作用自反算子代数的结构，并将J.Ringrose的套代数视为这类代数的原型。一个固定的冯诺依曼代数和一个完整的巢中所载的投影一个关联的代数的所有运营商在冯诺依曼代数离开每一个成员的巢不变。推广的Ringrose准则包含在Jacobson根的套代数给出了这类更一般的代数。进一步的自由基的性质进行了研究。
The structure of a certain class of separably acting reflexive operator algebras is investigated for which the nest algebras of J. Ringrose can be considered prototypes. To a fixed von Neumann algebra and a complete nest of projections contained therein one associates the algebra of all operators in the von Neumann algebra which leave every member of the nest invariant. A generalization of the Ringrose criterion for inclusion in the Jacobson radical of a nest algebra is given for this more general class of algebras. Further properties of the radical are studied.