The Study Of The Nature Of Numerical Domains And Positive Linear Mapping

Based on Hilbert right β-mode,we established four operator inequalities and obtained the kato and Farmland inequality as special example.We also extend it into numerical inequality radius and series.According to the content of this article is divided into the following four chapters.The first chapter summarizes the Hilbert right β-module and the relevant basic knowledge and theory origin.In the second chapter,we obtain four important properties of the operator vector inequalities and conclusion.In the third chapter,we obtain the norm inequality and numerical radius.In the fourth chapter,we discuss the series inequalities.