论文标题
$ m $ isometries的wold型分解
The Wold-type decomposition for $m$-isometries
论文作者
论文摘要
本文的目的是研究$ m $ isometries类中的Wold型分解。我们的主要结果之一为分析性$ m $ ismemetry提供了同等条件，以承认$ m \ ge2 $的Wold型分解。特别是，我们介绍了$ k $ - 内凯尔尼条件，我们用来表征分析性$ m $ iSometric运算符，该操作员单位等同于单方面运算符，价格为$ M \ ge2 $。结果，我们还表明，在有向图上的$ M $ iSometric构图运算符，一个电路中只有一个元素，并不等于单方面加权偏移。我们还提供了$ M $ - 等级单侧运算符的表征，并具有积极和通勤的权重。
The aim of this paper is to study the Wold-type decomposition in the class of $m$-isometries. One of our main results establishes an equivalent condition for an analytic $m$-isometry to admit the Wold-type decomposition for $m\ge2$. In particular, we introduce the $k$-kernel condition which we use to characterize analytic $m$-isometric operators which are unitarily equivalent to unilateral operator valued weighted shifts for $m\ge2$. As a result, we also show that $m$-isometric composition operators on directed graphs with one circuit containing only one element are not unitarily equivalent to unilateral weighted shifts. We also provide a characterization of $m$-isometric unilateral operator valued weighted shifts with positive and commuting weights.
