保持算子?-乘积幂等性的映射  

Mappings Preserving the Idempotency of ?- Product of Operators

作　　者：董改芳 DONG Gai-fang(Shuozhou Advanced Normal College,Shuozhou 036002,Shanxi,China)

机构地区：[1]朔州师范高等专科学校

出　　处：《山西师范大学学报（自然科学版）》2019年第4期1-4,共4页Journal of Shanxi Normal University(Natural Science Edition)

摘　　要：设H是复的完备的不定内积空间,dim H≥3,B(H)是由H上所有有界线性算子构成的代数,ΩB(H),I∈Ω,C^*I 1(H)Ω,且A∈Ω,G cv{A,I}Ω.本文主要对Ω上保持算子?-乘积幂等性的映射进行了完整的刻画.当H为Hilbert空间时,作为推论,给出了Ω上保持算子*乘积幂等性的映射的完整刻画.Let H be a complex completely indefinite inner product spaces,dim H≥3.Let B(H)be the sets of all linear operators on H.LetΩbe a subset of B(H),which containing at least all nonzero scalar multiples of rank-one idempotents and I,and G cv{A,I}Ωfor any A∈Ω.The maps preserving the idempotency of-product of operators onΩare characterized.Consequently,if H is a Hilbert spaces,the maps preserving the idempotency of*product of operators onΩare completely classified.

关 键 词：不定内积空间 幂等性 算子-乘积 算子*乘积 

分 类 号：O177[理学—数学]