论文标题
关于特定四载鼠收缩家族扩张的注释
A note on the dilation of a certain family of tetrablock contractions
论文作者
论文摘要
我们发现，在封闭的单位光盘中，由参数$α$索引的每个成员$（A_α，b，p）的显式四层等距扩张（仅封闭单位光盘索引（仅tetrablock contraction的第一个操作员取决于参数）。任何家庭成员的扩张空间都是相同的。也构建了上述每个家庭成员的伴随四载体收缩$（a_α^*，b^*，p^*）$的显式扩张。这个示例很重要，因为在文献中已经声称该示例没有扩张。从该构造中获取提示，并在$ h^2 _ {\ Mathbb d}上使用Toeplitz运算符（\ Mathcal d_p）$，我们获得了四载岩收缩的必要条件，以具有某种类型的四型四载等等速度扩张。
We find an explicit tetrablock isometric dilation for every member $(A_α, B, P)$ of a family of tetrablock contractions indexed by a parameter $α$ in the closed unit disc (only the first operator of the tetrablock contraction depends on the parameter). The dilation space is the same for any member of the family. Explicit dilation for the adjoint tetrablock contraction $(A_α^*, B^*, P^*)$ for every member of the family mentioned above is constructed as well. This example is important because it has been claimed in the literature that this example does not have a dilation. Taking cue from this construction and using Toeplitz operators on $H^2_{\mathbb D}(\mathcal D_P)$, we obtain necessary and sufficient conditions for a tetrablock contraction to have a certain type of tetrablock isometric dilation.
