Extension and inversion of extended orthomorphisms on Riesz spaces

Journal of the Australian Mathematical Society

Michel Duhoux¹ 

[1] Mathieu Meyer

关键词: 06 F 20;    46 A 40;    47 H 07;   

DOI  :  10.1017/S1446788700022059

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Let E be an Archimedean Riesz space and let Orth∞(E) be the f-algebra consisting of all extended orthomorphisms on E, that is, of all order bounded linear operators T:D→E, with D an order dense ideal in E, such that T(B∩D) ⊆ B for every band B in E. We give conditions on E and on a Riesz subspace F of E insuring that every T ∈ Orth∞(F) can be extended to some∈ Orth∞(E), and we also consider the problem of inversing an extended orthomorphism on its support. The same problems are also studied in the case of σ-orthomorphisms, that is, extended orthomorphisms with a super order dense domain. Furthermore, some applications are given.

【 授权许可】

Unknown