论文标题
关节向后扩展特性，用于在有向树上的加权转移
Joint backward extension property for weighted shifts on directed trees
论文作者
论文摘要
在有向树上的加权偏移是序列空间中经典移位运算符的十年旧概括$ \ ell^2 $。在本文中，我们将关节向后扩展属性（JBEP）引入了定向树上的加权转移类别。如果一类满足JBEP，则在同类中，在植根的有向树上的加权转移家族中存在一个共同的向后扩展，并不取决于大树的附加结构（固定深度）。我们决定几类运营商是否具有JBEP。对于亚正常或功率不正常的加权转移，则满足了特性，而完全过度刺激性或准确性失败。然而，证明了完全过度过度加权转移的联合向后扩展的一些积极结果。
Weighted shifts on directed trees are a decade old generalisation of classical shift operators in the sequence space $\ell^2$. In this paper we introduce the joint backward extension property (JBEP) for classes of weighted shifts on directed trees. If a class satisfies JBEP, the existence of a common backward extension within the class for a family of weighted shifts on rooted directed trees does not depend on the additional structure of the big tree (of fixed depth). We decide whether several classes of operators have JBEP. For subnormal or power hyponormal weighted shifts the property is satisfied, while it fails for completely hyperexpansive or quasinormal. Nevertheless some positive results on joint backward extensions of completely hyperexpansive weighted shifts are proven.
