Research On Young-type And Heinz-type Inequalities

Operator theory originated in the 20th century and is an important part of functional analysis.Now,it is applied in many fields,such as matrix theory,cybernetics,big data,etc.As a branch of operator theory,Young inequality is very important in the field of functional analysis.The research on Young inequality has attracted a large number of scholars.In this dissertation,Young inequality,Young type inequalities,reverse Young type inequalities and Heinz inequality are studied.On this basis,some norm inequalities including numerical radius and unitary invariant norm are derived and their generalizations are given.The main structure of this dissertation is as follows1.The research background,existing classical inequalities and lemmas of this disserta-tion are given,and the research results of many scholars at home and abroad are presented for the purpose of comparison in the following studies2.Mathematical methods are used to improve Young inequality,Young type inequali-ties,reverse Young type inequalities and Heinz inequality,including specht-ratio ratio and Kontorovich constant,as well as iterative method,and the inequality of partial Numbers is extended to the form of operator inequality.At the end of this part,some convex function inequalities are presented3.Generalize some norm inequalities,show some numerical radius inequalities and uni-tary invariant norm inequalities and improve Heinz inequality,hermit-hadaward inequality and cauchy-schwartz inequality on this basis.