On Some Operator Inequalities

This dissertation mainly study the refinements of several kinds of operator inequalities on Hilbert space,which are divided into four parts.The first chapter mainly introduce the research background of operator inequalities,besides,some notations and basic theorems are given.At the same time,it also give some existing inequalities related to this research.The second chapter obtain a series of Young type inequality for operators by using iteration and mathematical induction method.Firstly,it give a general formula of operator Young inequality;secondly,it discuss the Young type inequality of Kantorovich constant;finally,it also get the reverse Young type inequality of Specht ratio.The third chapter presents some Hilbert-Schmidt norm inequalities and operator mean inequalities under unit positive linear mapping by extending mean inequalities of operators.The fourth chapter introduce some equivalent conclusions of the parallelogram law,and extend it to the operator domain,thus a series of operator inequalities are obtained.