摘要
设A和B为无限维复Banach空间上的标准算子代数,记Δ~R(·)为下列谱函数之一:σ~R(·),σ_l^R(·),σ_r^R(·),σ_l^R(·)∩σ_r^R(·),(?)σ~R(·),(?)σ~R(·),σ_p^R(·),σ_c^R(·),σ_(ap)~R(·),σ_s^R(·),σ_(ap)~R(·)∩σ_s^R(·),σ_p^R(·)∩σ_c^R(·),σ_p^R(·)∪σ_c^R(·),其中R=A或B.证明了A和B之间的每个保持算子Jordan三乘积(算子乘积)之谱函数△~R(·)的满射Φ必有形式Φ=(?)π,其中(?)是1的立方根(1的平方根)而π或者是A和B之间的代数同构,或者是代数反同构.也获得不定度规空间上的标准算子代数之间保持算子斜乘积之谱函数的映射的完全刻画.
Let A and B be standard operator algebras on infinite-dimensional complex Banach spaces, Δ^R (·) be any one of the spectral functions σ^R (·), σl^R(·), στ^R (·), σl^R (·) ∩στ^R (·), δσ^R(·), σp^R(·), σc^R(·),σap^R(·),σs^R(·), σap^R(·)∩σs^R(·),σp^R (·)∩ σc^R(·) and σp^R(·)∪σc^R(·), where R=A or B. The authors show that every surjective map between .A and B which preserves the spectral function Δ^R (·) of Jordan triple-products (resp., products) of operators is either an isomorphism multiplied by a cubic root of 1 (resp. a square root of 1) or an anti-isomorphism multiplied by a cubic root of 1 (resp., a square root of 1). The surjective maps preserving the spectral function Δ^R(·) of skew products of operators between standard operator algebras on indefinite inner product spaces are also characterized.
出处
《数学年刊(A辑)》
CSCD
北大核心
2007年第6期769-780,共12页
Chinese Annals of Mathematics
基金
国家自然科学基金(No.10471082)
山西省自然科学基金(No.20021005)资助的项目.
关键词
标准算子代数
谱函数
算子乘积
算子斜乘积
Jordan代数同构
Standard operator algebra, Spectral functions, Jordan triple-products of operators, Skew products of operators, Jordan isomorphisms