有限秩算子及n-自反性

FINITE_RANK OPERATORS AND n _REFLEXIVITY

主要工作：（１）设Ｓ是向量空间Ｖ上的有限维线性算子空间，ＳＦ表示Ｓ中全体有限秩算子，则Ｓ是ｎ＿代数自反的等价于ＳＦ是ｎ＿代数自反的；（２）Ｓ是Ｂａｎａｃｈ空间Ｘ上的连续线性算子空间，当Ｓ满足一定条件时。

In this paper two results given by D. Larson are generalized. First, let S be a finite dimensional linear subspace of the algebra of all linear operators form vector space V into itself, and let S F denote the space of all finite_rank operators in S , then S is n _algebraically reflexive iff S F is n _algebraically reflexive. Second, let S be a linear subspace of the algebra of all continuous linear operators on a Banach space X , then S is n _topologically algebraically reflexive iff S F is n _topologically algebraically reflexive when S satisfies some properties.