局部紧群上取值在算子代数中的正定函数

Positive Definite Function from a Locally Compact Abelian Group to a C Algebra

把有关数值连续正定函数表示的Ｂｏｃｈｎｅｒ定理推广到更一般的情形，并将证明从一个局部紧交换群到一个Ｃ＊－代数的连续正定函数能够表示为向量值正测度的Ｆｏｕｒｉｅｒ变换．局部紧交换群到Ｃ＊－代数的连续正定函数对Ｃ＊－代数上的广义函数有重要作用．同时给出一个具体应用，推广Ｂｏｃｈｎｅｒ－Ｓｃｈｗａｒｔｚ定理至算子代数情形，得到Ｓ′（Ａ）上正定广义函数θ能表示为（θ，φ）＝∫φ（λ）ｄμ（λ）．

In relation to the representation of positive definite function on numerical value,the author extends its Bochner theorem to the more general situation.As it will be proved,the continuous positive definite function from a locally compact Abel group to a C * algebra can be represented as Fourier transform of vectrovalued positive measure;and the continuous positive definite function from locally compact Abel groups to C * algebra will play an important role in geeneralized function of C * algebra.Moreover,a specific application is given.Bochner schwartz theorem is extented to C * algebra ,and the positive definite generalized function θ can be represented as ( θ,φ)= ∫ (λ) d μ(λ)