Fock-Sobolev空间上复合算子集合的拓扑结构

Topological Structure of the Set of Composition Operators on Fock-Sobolev Spaces

本文研究多变量Fock-Sobolev空间上复合算子集合在不同范数下的拓扑结构.特别地,本文证明了此空间上复合算子集合中算子范数拓扑下的孤立点在本性范数拓扑下也是孤立的,并且对任意的0<p<∞,所有紧复合算子在Schatten p-范数拓扑下构成一个道路连通分支.

In this paper, we consider the topological structure of the set of compo- sition operators acting on Fock-Sobolev spaces of several variables in various norm topologies. Especially, we show that a composition operator that is isolated in the operator norm topology is also isolated in the essential norm topology, and all compact composition operators form a path component in the Schatten p-norm topology for each 0 〈 p 〈∞.