论文标题
加权构图操作员在离散加权的Banach空间上
Weighted composition operators on discrete weighted Banach spaces
论文作者
论文摘要
我们介绍了对加权组合算子的研究，在无限局部有限的公制空间的加权Banach空间上。具体而言，我们确定有限和紧凑的加权组成算子（包括操作员和基本规范）的特征。此外，我们表征了具有内色调的加权组成算子，在下面有封闭范围，并且具有相反的边界。我们表征了加权组成算子之间的异构体和滤波异构体，以及满足弗雷德霍尔姆条件的异构体。最后，我们提供了许多有趣的例子，说明了这些操作员在离散加权Banach空间上作用的丰富性。
We present the current results in the study of weighted composition operators on weighted Banach spaces of an unbounded, locally finite metric space. Specifically, we determine characterizations of bounded and compact weighted composition operators, including the operator and essential norms. In addition, we characterize the weighted composition operators that are injective, are bounded below, have closed range, and have bounded inverse. We characterize the isometries and surjective isometries among the weighted composition operators, as well as those that satisfy the Fredholm condition. Lastly, we provide numerous interesting examples of the richness of these operators acting on the discrete weighted Banach spaces.
