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.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.

arXiv:0903.5115Mar 30, 20090 citations

Remarks on Effect Algebras

W. A. Majewski, Tomasz I. Tylec

International Journal of Theoretical PhysicsDec 15, 20091 citation

Not each sequential effect algebra is sharply dominating

Jun Shen, Junde Wu

Let $E$ be an effect algebra and $E_S$ be the set of all sharp elements of $E$ . $E$ is said to be sharply dominating if for each $a\in E$ there exists a smallest element $\widehat{a}\in E_s$ such that $a\leq \widehat{a}$ . In 2002, Professors Gudder and Greechie proved that each $σ$ -sequential effect algebra is sharply dominating. In 2005, Professor Gudder presented 25 open problems in International Journal of Theoretical Physics, Vol. 44, 2199-2205, the 3th problem asked: Is each sequential effect algebra sharply dominating? Now, we construct an example to answer the problem negatively.Let $E$ be an effect algebra and $E_S$ be the set of all sharp elements of $E$. $E$ is said to be sharply dominating if for each $a\in E$ there exists a smallest element $\widehat{a}\in E_s$ such that $a\leq \widehat{a}$. In 2002, Professors Gudder and Greechie proved that each $σ$-sequential effect algebra is sharply dominating. In 2005, Professor Gudder presented 25 open problems in International Journal of Theoretical Physics, Vol. 44, 2199-2205, the 3th problem asked: Is each sequential effect algebra sharply dominating? Now, we construct an example to answer the problem negatively.

arXiv:0812.2502Dec 12, 20081 citation

Effect test spaces and effect algebras

Stanley Gudder

Foundations of PhysicsFeb 1, 199712 citations

Moment problem for effect algebras

Miloslav Duchoň, Anatolij Dvurečenskij, Paolo De Lucia

International Journal of Theoretical PhysicsSep 1, 19975 citations

Not each sequential effect algebra is sharply dominating

Shen Jun, Junde Wu

Let $E$ be an effect algebra and $E_S$ be the set of all sharp elements of $E$ . $E$ is said to be sharply dominating if for each $a\in E$ there exists a smallest element $\widehat{a}\in E_s$ such that $a\leq \widehat{a}$ . In 2002, Professors Gudder and Greechie proved that each $\sigma$ -sequential effect algebra is sharply dominating. In 2005, Professor Gudder presented 25 open problems in International Journal of Theoretical Physics, Vol. 44, 2199-2205, the 3th problem asked: Is each sequential effect algebra sharply dominating? Now, we construct an example to answer the problem negatively.Let $E$ be an effect algebra and $E_S$ be the set of all sharp elements of $E$. $E$ is said to be sharply dominating if for each $a\in E$ there exists a smallest element $\widehat{a}\in E_s$ such that $a\leq \widehat{a}$. In 2002, Professors Gudder and Greechie proved that each $\sigma$-sequential effect algebra is sharply dominating. In 2005, Professor Gudder presented 25 open problems in International Journal of Theoretical Physics, Vol. 44, 2199-2205, the 3th problem asked: Is each sequential effect algebra sharply dominating? Now, we construct an example to answer the problem negatively.

Jan 1, 20090 citations

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.

Let

E

be an effect algebra and

E_S

be the set of all sharp elements of

E

E

is said to be sharply dominating if for each

a\in E

there exists a smallest element

\widehat{a}\in E_s

such that

a\leq \widehat{a}

. In 2002, Professors Gudder and Greechie proved that each

σ

-sequential effect algebra is sharply dominating. In 2005, Professor Gudder presented 25 open problems in International Journal of Theoretical Physics, Vol. 44, 2199-2205, the 3th problem asked: Is each sequential effect algebra sharply dominating? Now, we construct an example to answer the problem negatively.

Let

E