论文标题
关于Hilbert $ C^*$ - 模块功能的扩展性
On extendability of functionals on Hilbert $C^*$-modules
论文作者
论文摘要
令$ m \子集n $为hilbert $ c^*$ - $ c^*$ - 代数$ a $，带有$ m^\ perp = 0 $。 J. Kaad和M. Skeide最近表明，存在非零$ a $ a $ a $ n $的功能，使其限制到$ m $为零。在这里，我们表明，即使$ a $是单调完成的，也可能会发生这种情况。另一方面，我们表明对于某些类型的I $ W^*$ - 代数不可能发生。
Let $M\subset N$ be Hilbert $C^*$-modules over a $C^*$-algebra $A$ with $M^\perp=0$. It was shown recently by J. Kaad and M. Skeide that there exists a non-zero $A$-valued functional on $N$ such that its restriction onto $M$ is zero. Here we show that this may happen even if $A$ is monotone complete. On the other hand, we show that for certain type I $W^*$-algebras this cannot happen.
