论文标题
常见的减少子空间和宫缩分解
Common reducing subspaces and decompositions of contractions
论文作者
论文摘要
希尔伯特太空运营商的三重通勤$（a，b，p）$，封闭的四载tetrablock $ \ operline {\ mathbb e} $是一个频谱集，称为a \ textit {tetrableock-contraction}或仅仅是$ \ \ m textiT { e = \ {（x_1，x_2，x_3）\ in \ mathbb c^3：\，1-x_1z-x_2w+x_3zw+x_3zw \ neq 0 \ quad \ quad \ text \ text {eyhe eection} \; | z | \ leq 1，\; \; | w | \ leq 1 \} \ subset \ mathbb c^3，\]是一个多项式凸域，自然与$μ$ - 同伴问题相关。根据$ \ Mathbb e $ $ - 扣除理论的应用，我们获得了有关收缩分解的几个结果。
A commuting triple of Hilbert space operators $(A,B,P)$, for which the closed tetrablock $\overline{\mathbb E}$ is a spectral set, is called a \textit{tetrablock-contraction} or simply an $\mathbb E$-\textit{contraction}, where \[ \mathbb E=\{(x_1,x_2,x_3)\in \mathbb C^3:\, 1-x_1z-x_2w+x_3zw \neq 0 \quad \text{ whenever } \; |z|\leq 1, \; \; |w|\leq 1 \} \subset \mathbb C^3, \] is a polynomially convex domain which is naturally associated with the $μ$-synthesis problem. By applications of the theory of $\mathbb E$-contractions, we obtain several results on decompositions of contractions.
