Multiplication Operators on Weighted Banach Spaces of a Tree
Multiplication Operators on Weighted Banach Spaces of a Tree
复制标题
树的加权 Banach 空间上的乘法运算符
DOI：
10.4134/bkms.b160007
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
I. Sundberg
中科院分区：
文献类型：
--
作者：
R. F. Allen;I. Sundberg
我们研究无限树的加权巴纳赫空间上的乘法运算符。我们描述有界算子和紧算子的特征，并确定算子范数。此外，我们还确定了有界乘法算子的谱并表征了等距性。最后，我们通过表征有界算子和紧算子来研究加权 Banach 空间和 Lipschitz 空间之间的乘法算子，确定算子范数的估计，并证明不存在等距性。
We study multiplication operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm. In addition, we determine the spectrum of the bounded multiplication operators and characterize the isometries. Finally, we study the multiplication operators between the weighted Banach spaces and the Lipschitz space by characterizing the bounded and the compact operators, determine estimates on the operator norm, and show there are no isometries.