工程数学学报
工程數學學報
공정수학학보
CHINESE JOURNAL OF ENGINEERING MATHEMATICS
2012年
1期
154-158
,共5页
τ-期望%τ-方差%τ-协方差%C*-代数
τ-期望%τ-方差%τ-協方差%C*-代數
τ-기망%τ-방차%τ-협방차%C*-대수
τ-expectation%τ-variance%τ-covariance%C*-algebra
引入了有单位元的C*-代数A的元素A的τ-期望Expτ(A)与τ-方差Varτ(A),它们分别定义为Expτ(A)=τ(A)与Varτ(A)=Expτ((A - Expτ(A)1AI)2),建立了关于它们的若干等式与不等式,给出了Expτ(AB)-Expτ(A)Expτ(B)与Varτ(A+ B)- Varτ(A)+ Varτ(A)的一些估计.引入并研究了元素A,B的τ-协方差Covτ(A,B),研究了元素的τ-独立性.
引入瞭有單位元的C*-代數A的元素A的τ-期望Expτ(A)與τ-方差Varτ(A),它們分彆定義為Expτ(A)=τ(A)與Varτ(A)=Expτ((A - Expτ(A)1AI)2),建立瞭關于它們的若榦等式與不等式,給齣瞭Expτ(AB)-Expτ(A)Expτ(B)與Varτ(A+ B)- Varτ(A)+ Varτ(A)的一些估計.引入併研究瞭元素A,B的τ-協方差Covτ(A,B),研究瞭元素的τ-獨立性.
인입료유단위원적C*-대수A적원소A적τ-기망Expτ(A)여τ-방차Varτ(A),타문분별정의위Expτ(A)=τ(A)여Varτ(A)=Expτ((A - Expτ(A)1AI)2),건립료관우타문적약간등식여불등식,급출료Expτ(AB)-Expτ(A)Expτ(B)여Varτ(A+ B)- Varτ(A)+ Varτ(A)적일사고계.인입병연구료원소A,B적τ-협방차Covτ(A,B),연구료원소적τ-독립성.
The expectation Expτ (A) and the variance Varτ (A) of an element A of a unital C*-algebra A with respect to a given state τ of A are defined as Expτ(A) =τ(A) and Varτ(A) =Expτ((A- Expτ(A)1A)2).Some equalities and inequalities about the expectations and the variances are established.Especially,some estimates of the difference of Expτ(AB)and Expτ(A)Expτ(B),Varτ(A + B) and Varτ(A) + Varτ(A) are obtained,respectively.Moreover,the τ-covariance Covτ(A,B) of A,B is introduced and the τ-independence of two elements is characterized.
