效应代数的同态
HOMOMORPHISM ON EFFECT ALGEBRAS

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.
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)