Product of Composition and Multiplication Operator

Abstract

Operators are nothing but the mapping from a topological space to a topological space. When it satisfies the criterion for the linearity, it becomes linear. So, composition and multiplication operators are certain type of operators and are bounded on a space called as Orlicz space which is the subject of consideration here. The composition operator CT and the multiplication operator Mu together multiplied to give a new operator named as Weighted composition operator Wu;T = CTMu given by f 7! u T:f T, on the Orlicz space. The thesis discusses various properties of the operator Wu;T starting with basic necessary preliminaries. Measurable set and functions are the necessary part of defining any domain. The property especially boundedness of the weighted composition operators are verified.