套代数中的初等算子

Elementary Operators on Nest Algebras

讨论了初等算子MAB(T) =ATB ,其中A、B∈T(N) ,MAB:T (N)→T (N) ;证明了MAB可逆当且仅当A和B在T(N)中均可逆 ,同时给出了MAB为单。

In this paper,We discuss M AB (T)=ATB,A,B∈T(N),M AB ∶T(N)→T(N);prove that M AB is invertible iff both A and B are invertible in T(N),and also give some necessary and sufficient conditions of which M AB is injective or M AB is surjective.