关于非分配子空间格与自反算子代数的若干性质

ON NON-DISTRIBUTIVE LATTICES OF SUBSPACES AND THE CORRESPONDING REFLEXIVE OPERATOR ALGEBRAS

首先给出 Hilbert 空间上的一个双三角格,使自反代数 alg含有限秩算子但 Lat(alg)不是 s-格,并给出 alg为 s-格的一个充要条件;其次讨论典型的五元素非分配子空间格对应自反算子代数,给出超自反性,有限秩稠性等一些结果.

This paper constructs a double triangleon a Hilbert space such that the reflexive algebra algcontains finite rank operators but Lat(alg)is not a s-lattice.An necessary and sufficient condition for Lat(alg )to be a s-lattice is also given.It also gives the hyperreflexivity,finite rank density for the reflexive algebras determined by pentagon ang double triangle on a Hilbert space.