自伴算子代数上的某些*-自同态的σ-弱混合性

σ-Weak Mixing of Certain *-Endomorphism of Self-Adjoint Operator Algebras

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, α b a＊- endomorphism of A. If there exists a unit element e ∈H such that limn→∞（α^n（α）h, h） = （αe, e） for all α A and h c H with ｜｜h｜｜ = 1, then we say α is a-weak mixing with respect to A. In this paper, we establish a condition for an ＊-endomorphism to be σ-weak mixing.