论文标题
Ando扩张的概括，以及一类$ Q $征收收缩的等级扩张
A generalization of Ando's dilation, and isometric dilations for a class of tuples of $q$-commuting contractions
论文作者
论文摘要
给定一个有界的运算符$ q $在hilbert space $ \ mathcal {h} $上，一对有界的操作员$（t_1，t_2）$上的$ \ nathcal {h} $ a说是$ q $ - cmumuting，如果以下一个： \ [ t_1t_2 = qt_2t_1 \ text {或} t_1t_2 = t_2qt_1 \ text {或} t_1t_2 = t_2t_1q。 \]我们为单一$ Q $的$ Q $ $ Q $征收收缩对等轴测扩张进行了明确的构造，该收缩概括了Ando [2]的等距扩张[2]。特别是，对于$ q = qi _ {\ mathcal {h}} $，其中$ q $是模量$ 1 $的复杂数量，这使得，作为推论，这是对$ q $ $ q $ cumpontration for actsotrary的明确结构。对于一般运营商的总体，有一个$ Q $ - 交易的概念，众所周知，等距扩张通常不适合$ n $ q $ $ q $ - 承诺的收缩，其中$ n \ geq 3 $。概括了Brehmer [8]考虑的通勤收缩等级，我们构建了$ n $ t的$ n $ tuplass $ q $ - 承诺收缩，并明确地找到了班级的等距扩张。
Given a bounded operator $Q$ on a Hilbert space $\mathcal{H}$, a pair of bounded operators $(T_1, T_2)$ on $\mathcal{H}$ is said to be $Q$-commuting if one of the following holds: \[ T_1T_2=QT_2T_1 \text{ or }T_1T_2=T_2QT_1 \text{ or }T_1T_2=T_2T_1Q. \] We give an explicit construction of isometric dilations for pairs of $Q$-commuting contractions for unitary $Q$, which generalizes the isometric dilation of Ando [2] for pairs of commuting contractions. In particular, for $Q=qI_{\mathcal{H}}$, where $q$ is a complex number of modulus $1$, this gives, as a corollary, an explicit construction of isometric dilations for pairs of $q$-commuting contractions which are well studied. There is an extended notion of $q$-commutativity for general tuples of operators and it is known that isometric dilation does not hold, in general, for an $n$-tuple of $q$-commuting contractions, where $n\geq 3$. Generalizing the class of commuting contractions considered by Brehmer [8], we construct a class of $n$-tuples of $q$-commuting contractions and find isometric dilations explicitly for the class.
