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| 摘要: |
| 本文研究了维数大于等于3的可分Hillbert空间H的效应代数E(H)上的同态问题.利用投影算子以及线性延拓的方法,获得了效应代数E(H)上每个满的σ-正交完备的强同态φ都具有形式φ(A)=U AU*,当满足齐次性以及单边保序的条件时可以延拓到交换von-Neumann代数A到B (H)上一个有界*同态的结果. |
| 关键词: 同态 效应代数 Von-Neumann代数 投影 Jordan*同态 |
| DOI： |
| 分类号:O177.1 |
| 基金项目:国家自然科学基金项目资助(11271224) |
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| HOMOMORPHISM ON EFFECT ALGEBRAS |
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ZHANG Hai-yan,HOU Cheng-jun
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| Abstract: |
| In this paper, we study the problems of homomorphics on the effect algebra E(H) of a separable Hillbert space H whose dimension is equal to or more than three. Using the projections and linear extension methods, we obtain that each surjective and strong σ-orthcomplete homomorphism has the form φ(A)=U AU*, and prove hat each homomorphism from E(A) into E(H) satisfying homogeneity and preserving order in one side can be extended to a bounded *-homomorphism from an abelian von-Neumann algebra A into B(H). |
| Key words: homomorphism effect algebra von-Neumann algebra projection Jordan * homomorphism |
