序列效应代数中的平均值不等式
The average value inequality in sequential effect algebras
摘要：
序列效应代数$(E,0,1, \oplus, \circ)$是在其上定义具有一定物理性质的序列积$\circ$的效应代数，特别是序列效应代数是研究量子测量理论的重要模型。2005年，Gudder提出了以下问题：如果$a, b\in (E,0,1,\oplus, \circ)$和$a\bot b$和$a\circ b\bot a\circ b$，那么是不是$2(a\circ b)\leq a^2\oplus b^2$的情况？在本文中，我们构造了一个例子来回答这个问题的负面影响。
英文摘要：
A sequential effect algebra $(E,0,1, \oplus, \circ)$ is an effect algebra on which a sequential product $\circ$ with certain physics properties is defined, in particular, sequential effect algebra is an important model for studying quantum measurement theory. In 2005, Gudder asked the following problem: If $a, b\in (E,0,1,\oplus, \circ)$ and $a\bot b$ and $a\circ b\bot a\circ b$, is it the case that $2(a\circ b)\leq a^2\oplus b^2$ ? In this paper, we construct an example to answer the problem negatively.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
