自反子空间格的表示和运算

Representations and operations on reflexive subspace lattices

证明了von Neumann代数的子空间格的自反性和KS-性都不依赖于该von Neumann代数的正规忠实*-表示;引入了von Neumann代数及所含子空间格的半自由积运算,证明了两子空间格的半自由积同构于它们的直和.

We show that the reflexivity of a subspace lattice in a von Neumann algebra is preserved under-isomorphism of the von Neumann algebra.A new operation,semi free product,of von Neumann algebras is introduced to study subspace lattices.Under this operation,the new subspace lattice is isomorphic to the direct product of the corresponding subspace lattices.