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Topological structure in the space of (weighted) composition operators on weighted Banach spaces of holomorphic functions
Bulletin des Sciences Mathématiques ( IF 1.3 ) Pub Date : 2019-10-24 , DOI: 10.1016/j.bulsci.2019.102806
Alexander V. Abanin , Le Hai Khoi , Pham Trong Tien

We consider the topological structure problem for the space of composition operators as well as the space of weighted composition operators on weighted Banach spaces with sup-norm. For the first space, we prove that the set of all composition operators that differ from the given one by a compact operator is path connected; however, in general, it is not always a component. Furthermore, we show that the set of compact weighted composition operators is path connected, but it is not a component in the second space.



中文翻译:

全纯函数加权Banach空间上(加权)合成算子空间中的拓扑结构

我们考虑了具有超范数的加权Banach空间上的复合算子空间以及加权复合算子空间的拓扑结构问题。对于第一个空间,我们证明所有组合运算符的集合(与紧凑运算符的给定运算符不同)是路径连接的;但是,通常它并不总是一个组件。此外,我们证明了紧凑加权合成算子的集合是路径连接的,但它不是第二空间中的一个分量。

更新日期:2019-10-24
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