论文标题
用约旦产品下的平均变换通勤地图
Commuting maps with the Mean Transform under Jordan product
论文作者
论文摘要
在本文中，我们对约旦产品下的平均变换通勤的徒图进行了完整的表征。主要结果是： 令$ h，k $是两个复杂的希尔伯特空间，$φ：b（h）\ to b（k）$是一张徒地图，然后 $$ \ MATHCAL {m}（φ（a）\ Circc（B））=φ（\ Mathcal {M}（A \ Circ B））\; \; \ text {for all} \; \; \; a，b \ in B（h）$$ 且仅当存在一个统一或反独立的操作员$ u：h \ to k $时， $$φ（t）= utu^* \; \ text {for All} \; t \ in B（h）。$$
In this article, we give a complete characterization of the bijective maps which commute with the mean transform under Jordan product. The main result is the following : Let $H,K$ be two complex Hilbert spaces and $Φ:B(H) \to B(K)$ be a bijective map, then $$ \mathcal {M}(Φ(A)\circΦ(B))=Φ(\mathcal{M}(A\circ B)) \;\; \text{for all}\;\; A, B \in B(H)$$ if and only if there exists a unitary or anti-unitary operator $U:H\to K $ such that, $$ Φ(T)= UTU^* \; \text{for all} \;T\in B(H).$$
