摘要
A sequential effect algebra （E, 0, 1, ,o） is an effect algebra on which a sequential product o 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 E （E, 0, 1, , o） and a⊥b and a o b⊥a o b, is it the case that 2（a o b） ≤ a2 b2 ？ In this paper, we construct an example to answer the problem negatively.
A sequential effect algebra （E, 0, 1, ,o） is an effect algebra on which a sequential product o 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 E （E, 0, 1, , o） and a⊥b and a o b⊥a o b, is it the case that 2（a o b） ≤ a2 b2 ？ In this paper, we construct an example to answer the problem negatively.
基金
Supported by Natural Science Fund of China (Grant Nos. 10771191 and 10471124)
