某些算子代数的可加导子

本文主要研究非Ｉｎ型因子ＶｏｎＮｅｕｍａｎｎ代数的Ｎｅｓｔ子代数及两元生成格自反代数的可加导子的自动线性性和连续性问题．通过给出一个含无限维交换ＶｏｎＮｅｕｍａｎｎ子代数的代数上可加导子定理，证明了非Ｉｎ型因子ＶｏｎＮｅｕｍａｎｎ代数的Ｎｅｓｔ子代数上的可加导子是线性的，从而是自动连续的．这推广并简化证明了作者［１］中的主要结果．对于在非自伴算子代数研究中起重要的两元生成格自反代数，给出了所有可加导子是线性导子的充分必要条件．

Additive Derivations of Certain Operator Algebras

In this paper we continue to study additive dervations of certain operator algebras.In section 2, we prove that every additive dervation of a nest-subalgebra of non-type In factor Von Neumann algebra is automatically continuous. This extends the main result of 1]. In section 3, we give a necessary and sufficient condition for which every additive dervation of two elements generated subspace lattice algebra is automatically linear.