Gardia, Sharata Charan (2015) *Product of Composition and Multiplication Operator.* MSc thesis.

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## 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.

Item Type: | Thesis ( MSc) |
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Uncontrolled Keywords: | Orlicz space,measurable space,measurable function,composition operator,multiplication operator,weighted composition operator,convex function,orlicz function,measurable transformaion,non-singular measurable transformation,Radon-NikodynTheorem |

Subjects: | Mathematics and Statistics > Topology |

Divisions: | Sciences > Department of Mathematics |

ID Code: | 6894 |

Deposited By: | Mr. Sanat Kumar Behera |

Deposited On: | 08 Mar 2016 15:09 |

Last Modified: | 08 Mar 2016 15:09 |

Supervisor(s): | Pradhan, S |

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