套代数弱闭模中的几何秩

由于几何秩在线性等距映射下是不变的,因此几何秩是研究算子代数线性等距映射的一个强有力的工具.证明了在一定条件下,套代数弱闭模中的n秩算子的几何秩的上、下界分别为n2和n(n+1)2,这表明套代数弱闭模中有限秩算子的充要条件是算子的几何秩有限.

Geometric rank in weakly closed modules of nest algebras

The geometric rank is a powerful tool in the study of isometries of operator algebras since the geometric rank is invariant under isometries. In the mild condition, it is proved that the lower bounder and the upper bounder of the geometric rank of a rank n operator in weakly closed modules of nest algebras are n~2 and n(n+1)]2 respectively, which implies that an operator in weakly closed modules of nest algebras is of finite rank if and only if its geometric rank is finite.