Study On Young Type Operator Inequalities With Kantorovich Constants And Singular Value Inequalities Of Matrices

The operator theory,produced in the early twentieth Century,plays an important role in the theory of functional analysis.Its main object is to define functions in any dimensional space.The research content is mainly the tightness,boundedness,spectral properties,algebraic and geometric properties of the bounded linear operators on Hilbert space.Since the 60 s of last century,the theory of operators has developed rapidly.It plays an important role in mathematical fields such as optimization theory,matrix theory and differential equation.In addition,it plays an important role in physics and other important fields.Because of the wide range of operator theory,it has formed its own logic system,attracting more and more scholars' research.In this paper,we mainly study the Young type operator inequalities with Kantorovich constant and the singular value inequalities of semi positive definite matrices,and make innovative improvements.The main contents are as follows:1.We mainly introduce the development process of operator inequalities,as well as some basic symbols and their representation of matrix symbols.2.We derive the scalar inequality of Young type inequality and its inverse by using the Kantorovich constant and its properties.3.We get the operator inequality of Young type and its inverse through the monotonicity principle of operator function.4.We obtain the matrix inequalities of Young type and its inverse by using the unitary invariance of Hilbert-Schmidt norm.5.Using the block matrix method and Weyl monotone theorem,we derive the new matrix singular value inequality.