Fan-Todd Inequality And The Research Of Matrix And Operator Inequality

The developed of matrix inequalities have offered us convenience for solving related inequalities problems of the operator theory.This paper obtains some results of matrix trace and operator trace through the study of property of matrix trace inequality and discusses some works on Furuichi conjecture on the basis of Tsallis entropy 、 Tsallis relative entropy and BMV conjecture.Main research of contents:The second part is the main content:The first part is a preface: the text introduced mainly knowledge background related to this topic,development condition and application at home and abroad,results made in recently years and many urgent issues to tackle.Chapter 1: notation and definition,it mainly presents mark and basic concepts of matrix and operator theory that are required.Chapter 2: types of business matrix trace inequalities.According to the four business real inequalities,promotion to the relate conclusions in the matrix theory.Chapter 3: Generations of Fan-Todd inequality in both matrix and operator theory.The principal content in this section,Fan-Todd inequality is promoted to operator theory from real number to new Matrix trace inequalities according to Cauchy-Schwarz inequality and its properties.