论文标题
可接受的基本运算符，与$ $ $ $合成相关的两个域相关
Admissible fundamental operators associated with two domains related to $μ$-synthesis
论文作者
论文摘要
在本文中，我们讨论了完全非单身（C.N.U）$γ_{n} $ - 收缩和C.N.U $ \ Mathbb e $ $ - $ $ - 合同的必要条件。考虑两个元组，$（a_1，\ dots，a_ {n-1}）$和$（b_1，\ dots，b_ {n-1}）$，在两个Hilbert Spaces上定义的操作员。主要目标之一是确定一个必要和足够的条件，以保证存在c.n.u $γ_n$ -contraction $（s_1，\ dots，s_ {n-1}，p）$ $（a_1，\ dots，a_1，\ dots，a_ {n-1}）$ s_ {n-1}，p）$和$（b_1，\ dots，b_ {n-1}）$变为$（s_1^*，\ dots，s_1^*，s_ {n-1}^*，p^*，p^*）$。同样在给定两对操作员$（f_1，f_2）$和$（g_1，g_2）$上定义在两个希尔伯特空间上的$，我们检查何时有一个c.n.u $ \ $ \ mathbb e $ -contraction $（a，b，p）$ $（g_1，g_2）$变为$ \ Mathcal {f} _O $ - $（a^*，b^*，p^*）$的$。
In this article, we discuss necessary condition of conditional dilation for both completely non-unitary (c.n.u) $Γ_{n}$-contractions and c.n.u $\mathbb E$-contractions. Consider two tuples, $(A_1, \dots, A_{n-1})$ and $(B_1, \dots, B_{n-1})$, of operators defined on two Hilbert spaces. One of the principal goals is to identify a necessary and a sufficient condition guaranteeing the existence of a c.n.u $Γ_n$-contraction $(S_1, \dots, S_{n-1},P)$ such that $(A_1, \dots, A_{n-1})$ becomes the $\mathcal{F}_O$-tuple of $(S_1, \dots, S_{n-1},P)$ and $(B_1, \dots,B_{n-1})$ becomes the $\mathcal{F}_O$-tuple of $(S_1^*,\dots, S_{n-1}^*,P^*)$. Also for given two pairs of operators $(F_1,F_2)$ and $(G_1,G_2)$ defined on two Hilbert spaces, we examine when there is a c.n.u $\mathbb E$-contraction $(A,B,P)$ such that $(F_1,F_2)$ becomes the $\mathcal{F}_O$-pair of $(A,B,P)$ and $(G_1,G_2)$ becomes the $\mathcal{F}_O$-pair of $(A^*,B^*,P^*)$.
