ISOMETRIC DILATIONS OF REPRESENTATIONS OF PRODUCT SYSTEMS VIA COMMUTANTS
ISOMETRIC DILATIONS OF REPRESENTATIONS OF PRODUCT SYSTEMS VIA COMMUTANTS
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DOI：
10.1142/s0129167x08004790
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发表时间：
2006-02
影响因子：
0.6
通讯作者：
Michael Skeide
中科院分区：
文献类型：
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作者：
Michael Skeide
构造了非单位CP-半群到作用于具有单位向量的Hilbert模的伴随算子的E-半群的弱扩张。我们构造了扩张的E-半群，使得扩张的E-半群有一个预先指定的乘积系统。然后，利用von Neumann对应的交换子，利用伸缩定理证明了乘积系统的协变表示允许等距伸缩。
We construct a weak dilation of a not necessarily unital CP-semigroup to an E-semigroup acting on the adjointable operators of a Hilbert module with a unit vector. We construct the dilation in such a way that the dilating E-semigroup has a pre-assigned product system. Then, making use of the commutant of von Neumann correspondences, we apply the dilation theorem to prove that covariant representations of product systems admit isometric dilations.