设A是希尔伯特空间H上的自伴算子代数,α是A上的*-自同态.如果存在单位向量e∈H,使得对任意α∈A和单位向量h∈H,有lim_(n→∞)〈α~n(a)h,h〉=〈αe,e〉成立,那么称α是A上的σ-弱混合的*-自同态.本文研究了这一有趣性质,并得到了一个*-自同态是σ-弱混合的充分条件.

Let A be a self-adjoint operator algebra of Hilbert space H,a be a*- endomorphism of A.If there exists a unit element e∈H such that lim_(→∞)〈α~n(a)h, h〉=〈ae,e〉for allα∈A and h∈H with‖h‖=1,then we sayαisσ-weak mixing with respect to A.In this paper,we establish a condition for an *-endomorphism to beσ-weak mixing.