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arXiv · 0903.5115

The average value inequality in sequential effect algebras

Shen Jun·Wu Junde
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Abstract

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.

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Shen Jun, Wu Junde. 2009-03-30. The average value inequality in sequential effect algebras. https://arxiv.org/abs/0903.5115

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