套子代数上的自伴线性映射

Hermitian linear mappings of nest subalgebras

研究了Ⅲ型因子von Neumann代数中套子代数上的自伴导子和自伴线性映射,证明了Ⅲ型因子von Neumann代数M中的任一套子代数algMβ上的每一个自伴导子都可表示为T→TA-AT,其中A是algMβ中的一个自伴算子.由此,Ⅲ型因子von Neumann代数M中的任一套子代数algMβ上的每一个自伴线性映射都可表示为T→TB-AT,其中A,B是algMβ中的两个自伴算子.

The hermitian derivations and hermitian linear mappings on any nest subalgebras （algMβ） of type Ⅲ factor von Neumann algebra are introduced, h is shown that every hermitian derivation of any nest subalgebras （algMβ） of type Ⅲ factor yon Neumann algebra is of the form T→TA - AT, where A is a self-adioint operator in the nest subalgebra（algMβ）, therefore, every hermitian linear mapping of any nest subalgebra（algMβ） of type Ⅲ factor yon Neumann algebra is of the form T→TB -AT, where A, B are two self-adjoint operators in the nest subalgebra（algMβ）.