保持算子Jordan-■-triple乘积幂等性的映射

Mappings Preserving the Idempotency of Jordan-■-triple Product of Operators

设H是无限维的复的完备的不定内积空间,B(H)是H上所有有界线性算子构成的代数,ΩB(H).本文主要刻画Ω上保持算子Jordan-?-triple乘积幂等性的映射.当H为Hilbert空间时,作为推论,给出了Ω上保持算子Jordan-*-triple乘积幂等性的映射的具体形式.

Let H be a infinite complex completely indefinite inner product spaces,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.The maps preserving the idempotency of Jordan-?-triple product of operators onΩare characterized.Consequently,if H is a Hilbert spaces,the maps preserving the idempotency of Jordan-*-triple product of operators onΩare completely classified.