In this paper,we introduce and investigate the mutual information and relative entropy on the sequentialeffect algebra,we also give a comparison of these mutual information and relative entropy with the classical ones...In this paper,we introduce and investigate the mutual information and relative entropy on the sequentialeffect algebra,we also give a comparison of these mutual information and relative entropy with the classical ones by thevenn diagrams.Finally,a nice example shows that the entropies of sequential effect algebra depend extremely on theorder of its sequential product.展开更多
Let （L, ,0, 1） be an effect algebra and let X be a Banach space. A function ： L→ X is called a vector measure if μ（a b） =μ（a） ＋ μ（b） whenever a⊥b in L. The function μ is said to be 8-bounded if limn...Let （L, ,0, 1） be an effect algebra and let X be a Banach space. A function ： L→ X is called a vector measure if μ（a b） =μ（a） ＋ μ（b） whenever a⊥b in L. The function μ is said to be 8-bounded if limn→∞μ（an） = 0 in X for any orthogonal sequence （an）n∈N in L. In this paper, we introduce two properties of sequence of s-bounded vector measures and give some results on these properties.展开更多
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...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.展开更多
We prove that sharply dominating Archimedean atomic lattice effect algebras can be characterized by the property called basic decomposition of elements.As an application we prove the state smearing theorem for these e...We prove that sharply dominating Archimedean atomic lattice effect algebras can be characterized by the property called basic decomposition of elements.As an application we prove the state smearing theorem for these effect algebras.展开更多
The famous Antoslk-Mlkusinskl convergent theorem on the Abel topological groups has very extensive applications In measure theory, summation theory and other analysis fields. In this paper, we establish the theorem on...The famous Antoslk-Mlkusinskl convergent theorem on the Abel topological groups has very extensive applications In measure theory, summation theory and other analysis fields. In this paper, we establish the theorem on a class of effect algebras equipped with the Ideal topology. This paper shows also that the Ideal topology of effect algebras is s useful topology In studying the quantum logic theory.展开更多
In the present paper the properties of morphisms in effect algebras are discussed. The conditions for the morphisms in effect algebras to be join-preservation and meet-preservation are given. From the categorical poin...In the present paper the properties of morphisms in effect algebras are discussed. The conditions for the morphisms in effect algebras to be join-preservation and meet-preservation are given. From the categorical point of view, some properties of ideals, filters and congruence relations under morphisms are obtained.展开更多
In this paper, we show that every weakly a uniform topology （weakly algebraic ideal topology, algebraic ideal of an effect algebra E induces for short） with which E is a first-countable, zero-dimensional, disconnect...In this paper, we show that every weakly a uniform topology （weakly algebraic ideal topology, algebraic ideal of an effect algebra E induces for short） with which E is a first-countable, zero-dimensional, disconnected, locally compact and completely regular topological space, and the operation ＋ of effect algebras is continuous with respect to these topologies. In addition, we prove that the operation - of effect algebras and the operations A and V of lattice effect algebras are continuous with respect to the weakly algebraic ideal topology generated by a Riesz ideal.展开更多
基金Supported by Research Foundation of Kumoh National Institute of Technology
文摘In this paper,we introduce and investigate the mutual information and relative entropy on the sequentialeffect algebra,we also give a comparison of these mutual information and relative entropy with the classical ones by thevenn diagrams.Finally,a nice example shows that the entropies of sequential effect algebra depend extremely on theorder of its sequential product.
文摘Let （L, ,0, 1） be an effect algebra and let X be a Banach space. A function ： L→ X is called a vector measure if μ（a b） =μ（a） ＋ μ（b） whenever a⊥b in L. The function μ is said to be 8-bounded if limn→∞μ（an） = 0 in X for any orthogonal sequence （an）n∈N in L. In this paper, we introduce two properties of sequence of s-bounded vector measures and give some results on these properties.
基金Supported by Natural Science Fund of China (Grant Nos. 10771191 and 10471124)
文摘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the National Natural Science Foundation of China (Grant Nos.10771191,10471124)the Natural Science Foundation of Zhejiang Province (Grant Nos.M103057,10771191)the Slovak Research and Development Agency under the contracts SK-CN-017-06 and APVV-0071-06
文摘We prove that sharply dominating Archimedean atomic lattice effect algebras can be characterized by the property called basic decomposition of elements.As an application we prove the state smearing theorem for these effect algebras.
基金Supported by the National Natural Science Foundation of China (Grant No. 20273050) the National High Technology Research and Devel-opment Program of China (Grant Nos. 2003AA2Z2031 and 2005AA205220)
文摘The famous Antoslk-Mlkusinskl convergent theorem on the Abel topological groups has very extensive applications In measure theory, summation theory and other analysis fields. In this paper, we establish the theorem on a class of effect algebras equipped with the Ideal topology. This paper shows also that the Ideal topology of effect algebras is s useful topology In studying the quantum logic theory.
基金the National-Natural Science Foundation of China （No. 10331010） the Natural Science Foundation of Fujian Province of China （No, 2006J0221）.
文摘In the present paper the properties of morphisms in effect algebras are discussed. The conditions for the morphisms in effect algebras to be join-preservation and meet-preservation are given. From the categorical point of view, some properties of ideals, filters and congruence relations under morphisms are obtained.
基金Supported by National Natural Science Foundation of China(Grant Nos.11401469 and 11171200)Shaanxi Province Natural Science Foundation(Grant No.2014JQ1032)
文摘In this paper, we show that every weakly a uniform topology （weakly algebraic ideal topology, algebraic ideal of an effect algebra E induces for short） with which E is a first-countable, zero-dimensional, disconnected, locally compact and completely regular topological space, and the operation ＋ of effect algebras is continuous with respect to these topologies. In addition, we prove that the operation - of effect algebras and the operations A and V of lattice effect algebras are continuous with respect to the weakly algebraic ideal topology generated by a Riesz ideal.
