The Density Problem Of Irreducible Operators In A Class Of AF Algebras

P.R.Halmos studied the problem of density of irreducible operators onB(H)in the 1960s,and proved that irreducible operators in B(H)are dense with respect to norm topology inB(H).In 2010,Fang Junsheng and Shi Rui extended the density problem of this irreducible operator to all types of factors,i.e.,for any factor M with predual properties(can be type Ⅰ,type Ⅱ,type Ⅲ).The set of irreducible operators in M is dense about norm topology.This result is of great help to solve the problem of factor.The theory and application of C*-algebras have a lot of relations in operator algebra,group representation,topology,dynamic system and so on.Since 1993,Elliott has been classifying C*-algebras using K theory.In recent years,the classification problem of C*-algebras has been deepened,but there is no in-depth research on this problem of C*-algebras,and we know that not all C*-algebras can study this kind of problem,so we hope to find a class of C*-algebras to realize this kind of problem.In this paper,we prove that irreducible operators in UHF algebras are dense in the sense of normal topology.