标准效应代数${\cal E} (H)$上的序列积
Sequential product on standard effect algebra ${\cal E} (H)$
摘要：
量子效应是复希尔伯特空间$H$上的算子$A$，满足$0\leq A\leq I$，${\cal E} (H)$是$H$上所有量子效应的集合。2001年，Gudder教授和Nagy研究了$A, B\in {\cal E}(H)$的序贯乘积$A\circ B=A^{1/2}BA^{1/2}$。2005年，Gudder教授问：$A\circ B=A^{1/2}BA^{1/2}$是${\cal E} (H)$上唯一的序贯产品吗？最近，刘和吴提出了一个例子来表明答案是否定的。本文首先刻画了${\cal E} (H)$上抽象序列积的一些代数性质;其次给出了构造${\cal E} (H)$上序列积的一般方法;最后研究了用这种方法构造的序列积的一些性质
英文摘要：
A quantum effect is an operator $A$ on a complex Hilbert space $H$ that satisfies $0\leq A\leq I$, ${\cal E} (H)$ is the set of all quantum effects on $H$. In 2001, Professor Gudder and Nagy studied the sequential product $A\circ B=A^{1/2}BA^{1/2}$ of $A, B\in {\cal E}(H)$. In 2005, Professor Gudder asked: Is $A\circ B=A^{1/2}BA^{1/2}$ the only sequential product on ${\cal E} (H)$? Recently, Liu and Wu presented an example to show that the answer is negative. In this paper, firstly, we characterize some algebraic properties of the abstract sequential product on ${\cal E} (H)$; secondly, we present a general method for constructing sequential products on ${\cal E} (H)$; finally, we study some properties of the sequential products constructed by the method
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