论文标题
von Neumann代数的近似等效性
Approximate Equivalence in von Neumann Algebras
论文作者
论文摘要
假设$ \ Mathcal {a} $是可分离的Unital Ash C*-Algebra，$ \ Mathcal {r} $是Sigma-Finite II $ _ {\ infty} $ factor von neumann algebra，$ von neumann algebra，$ p，$π，ρ：\ natercal {a} a} $ \ ast $ -HOLMORGOLISS，以便，对于\ Mathcal {a} $中的每一个$ a \，$π\ left（a \ right）$和$ρ\ left（a \ right）$的范围投影是Murray von Neuman等价的$ \ Mathcal {r} r} r}％$。我们证明，$π$和$ρ$大致是单位等效的模型$ \ Mathcal {k} _ {\ Mathcal {r}} $，其中$ \ Mathcal {k} _ {\ Mathcal {r Mathcal {r}} $是$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ rat。我们还证明了关于任意有限的von Neumann代数的近似等效性的非常普遍的结果。
Suppose $\mathcal{A}$ is a separable unital ASH C*-algebra, $\mathcal{R}$ is a sigma-finite II$_{\infty}$ factor von Neumann algebra, and $π,ρ:\mathcal{A}\rightarrow\mathcal{R}$ are unital $\ast$-homomorphisms such that, for every $a\in\mathcal{A}$, the range projections of $π\left( a\right) $ and $ρ\left( a\right) $ are Murray von Neuman equivalent in $\mathcal{R}% $. We prove that $π$ and $ρ$ are approximately unitarily equivalent modulo $\mathcal{K}_{\mathcal{R}}$, where $\mathcal{K}_{\mathcal{R}}$ is the norm closed ideal generated by the finite projections in $\mathcal{R}$. We also prove a very general result concerning approximate equivalence in arbitrary finite von Neumann algebras.
