Extension Of Kadison Inequality And Character Of The Chaotic Order

In this paper, we are based on the Kadison inequality and its generalization, we shallintroduce several new inequalities relative to some others operator inequalities. we intendto seperate this paper into three parts in order to introduce the problems relative to thispaper.The first part is introduction. We mainly introduce some related operator inequalitiesand background of this paper, besides, we also introduce some theorems and knowledgethat are referred frequently in this paper.The second part is the generalized styles of Kadison inequality. The part is separatedinto three small parts to introduce, which studies2、n+1operators’ inequality respectivelyand some notes of Kadison inequality and postive linear maps. We briefly prove theseinequalities and also talk about their diferences and relations.The third part introduce the character of operator chaotic order and its application.This part can be considered as the property associated with operator inequalities in thesecond part. This part not only enrich the concent of operator monotone function in theoperator theorem, but also make foundation for studying of the operator theorem.