Quasidiagonal C*-subalgebras of multi-plier algebras of certain C*-algebras

Based on the assumption that the C*-algebra I has an approximate unit consisting of projections, the paper presents a class of C*-subalgebras of M(I) with the C*-algebra I as an ideal. Every element of these given C*-subalgebras proves to be weakly quasidiagonal and there lationship among them is proved too. The paper also presents the answer to the lifting problems of the projections of the corresponding quotient C*-algebras.