| The study of the mean value is one of the more popular directions in operator algebra,which has attracted the attention of a large number of mathematicians and researchers since last century.Kubo,Ando,M.Bresar,Semrl,Anderson,Molnar particularly prominent scholars achievements.Common average such as geometric mean,arithmetic mean and harmonic mean are widely used.Later,Molnar and other scholars studied many other mean values,such as weighted geometric mean,the parameters of the mean,geodetic mean,Heron mean,Heinz mean,log-Euclide mean and described the forms of mappings preserving these mean values,thus it greatly promote the development of the average problem in operator algebra.In chapter 1,we give some basic knowledge of the operator algebra and means.In chapter 2,we mainly studies the mappings that preserve the norm of the weighted means on the positive cone of operator algebras.In section 1 of chapter 2,we first recall the development process of the means and the definition of the four kinds of means.In section 2 of chapter 2,we first introduce the structure and properties of the mapping on positive cone of the C*-algebra that preserves the norm of several weighted means.We then give some lemmas needed later.In section 3 of chapter 2,we consider the structure and properties of the mappings that preserve the p-norms of the weighted means on positive cone of C*-algebras.The results we obtained extend known results. |
