一类自反算子代数上的自伴线性映射

Hermitain linear mappings on certain reflexive operator algebras

研究了完全分配交换格代数和ＶｏｎＮｅｕｍａｎｎ代数中套子代数上的自伴线性映射．得到一类完全分配交换格代数上的自件线性映射均为Ｔ→ＡＴ—ＴＢ形式，其中Ａ和Ｂ为自伴算子．证明了有限因子ＶｏｎＮｅｕｍａｎｎ代数中套子代数上的自伴线性映射也可表示为Ｔ→ＡＴ—ＴＢ，其中Ａ和Ｂ是套子代数的对角代数中的算子．

Hermitain linear maps on completely distributive CSL-algebras and nest -sbalgebras of Von Neumann algebras are discussed. The author obtain a class CSL-algebras and show that hermitian linear mapping on the CSL-algebra is of the form T→AT-TB,where A and B are hermitain operator. It is proved that hermitian linear mapping on nestsubalgebras of finite factor Von Neumann algebra is of the form T→KT-TS, where K and S belong to the diagonal of the nest-subalgebra.