算子权移位的亚自反性

Hyporeflexivity of Operator Weighted Shifts

本文首先仿照 A.Lambert 对单边算子权移位的处理方法刻划了双边算子权移位所张成的弱闭代数,进而证明了算子权移位均是亚自反的.做为推论,讨论了算子权移位直接和的自反性,从而在算子权移位范围内肯定回答了 J.Deddens 的两个问题.

Imitating A.Lambert' s method,we describe first weakly closed alge- bra generated by a bilateral operator weighted shift.Further,the hyporeflexivityof of operator weighted shifts is proved.As a result,we show if S and T are reflexive, operator weighted shifts then S⊕T is reflexive and S⊕S is reflexive for any opera- tor weighted shift S.