Distance Between Unitary Orbits Of Self-Adjoint Elements In Some C*-Algebras Of Tracial Rank No More Than One

This thesis mainly studies the distance between unitary orbits of normal elements in some C*-algebras.Let dist(U(x),U(y))denote the distance between unitary orbits of x and y.For matrix algebra Mn,let x,y ∈ Mn be two self-adjoint elements with eigenvalues {α1,...,αn} and {β1,...,βn} respectively.Suppose where π runs over all permutations of {1,...,n｝.H.Weyl proved that for any selfadjoint elements x,y ∈ Mn,dist(U(x),U(y))=δ(x,y).This thesis first obtains a result of the Riesz interpolation property,then obtains a generalization of H.Weyl’s theorem for two types of algebras,one type is C*-algebras of tracial rank no more than one,another type is C*-algebras of real rank zero and stable rank one.Specifically,for any self-adjoint elements x,y in unital AT-algebras or self-adjoint elements x,y in unital simple C*-algebras of tracial rank no more than one,this thesis proves that dist(U(x),U(y))=Dc(x,y),where D,(x,y)is anotationgeneralized from δ(x,y).For any self-adjoint elements x,y in C*-algebras of real rank zero and stable rank one,this thesis proves that dist(U(x),U(y))=D,(x,y).In addition,problems of the distance between unitary orbits of normal elements in some important C*-algebras is discussed,and the influence of hereditary C*-subalgebras for Dc is discussed.