Topological Properties Of Composition Operators And Integral Type Operators

In this paper, the object of study contains two categories: one is compositionoperator, and another is integral type operators.The research of composition operators involves two parts:Firstly, we characterize the boundedness and compactness of diferences of com-position operators from F (p, q, s) space to weighted Bloch space on the unit disk, andunder these conclusions, topological connectness of space of all bounded compositionoperators from F (p, q, s) to weighted Bloch space endowed with operator norm is inves-tigated.Secondly, we focused on the Hilbert-Schmidt diference and topological structureof composition operators on the classic Bergman space on the unit ball, and we use theextreme points of holomorphic self mappings of unit ball to study the isolated problem.For the integral type operator, we characterize the boundedness and compactness ofthese two integral operators, acting from the logarithmic Bloch-type space to F (p, q, s)space on the unit ball, and in the end, the properties of another two similar operatorsare given without proving.