论文标题
在树的加权Lipschitz空间上的乘法运算符
Multiplication operators on the weighted Lipschitz space of a tree
论文作者
论文摘要
我们研究了加权Lipschitz空间上的乘法运算符$ \ Mathcal {l} _ {\ textbf {w}} $由复杂值函数$ f $组成的无限树$ t $ t $ oted ot ot $ o $ o $ o $ o $ \ s op \ sup_ v \ v \ n neq \ neq \ neq \ n neq \ n n n n n n n n n neq o} | v || f（v）-f（v^ - ）| <\ infty $，其中$ | v | $表示$ o $和$ v $和$ v $和$ v^ - $是$ v $的邻居，最接近$ o $。对于乘法运算符，我们表征有界性，紧凑性，提供对操作员规范和本质规范的估计，并确定频谱。我们证明，$ \ Mathcal {l} _ {\ textbf {w}} $上没有等距乘法运算符或等轴测零除数。
We study the multiplication operators on the weighted Lipschitz space $\mathcal{L}_{\textbf{w}}$ consisting of the complex-valued functions $f$ on the set of vertices of an infinite tree $T$ rooted at $o$ such that $\sup_{v\neq o}|v||f(v)-f(v^-)|<\infty$, where $|v|$ denotes the distance between $o$ and $v$ and $v^-$ is the neighbor of $v$ closest to $o$. For the multiplication operator, we characterize boundedness, compactness, provide estimates on the operator norm and the essential norm, and determine the spectrum. We prove that there are no isometric multiplication operators or isometric zero divisors on $\mathcal{L}_{\textbf{w}}$.
