有限维Hilbert空间的强自反子空间格代数模的性质

THE REPRESENTATION (Ⅰ) OF FINITE RANK OPERATOR

定义了空间格代数的 (弱闭双边 )模 ,对有限维Hilber空间的强自反子空间格代数的模中的有限秩算子进行了讨论 ,得到有限秩算子一定可以表示为秩 1算子的和 .

The object of this paper is to study the finite rank operator in the weakly closed modules of the algebra of subspace lattice,and we obstain every operator of finite rank in the modules of the algebra of the finite Hilbert subspace lattices can be written as a finite sum of operator of rank one each belonging to the modules.