Orthomorphisms of a commutative W*-algebra

Journal of the Australian Mathematical Society

P. G. Dodds¹ 

关键词: 46 A 40;    47 B 55;   

DOI  :  10.1017/S1446788700021996

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

If M is a commutative W*-algebra of operators and if ReM is the Dedekind complete Riesz space of self-adjoint elements of M, then it is shown that the set of densely defined self-adjoint transformations affiliated with ReM is a Dedekind complete, laterally complete Riesz algebra containing ReM as an order dense ideal. The Riesz algebra of densely defined orthomorphisms on ReM is shown to coincide with , and via the vector lattice Randon-Nikodym theorem of Luxemburg and Schep, it is shown that the lateral completion of ReM may be identified with the extended order dual of ReM.

【 授权许可】

Unknown