Complex structures on real vector lattices

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:440

Article

Kusraeva, Z. A.^1,2 

[1] Markus St 22, Vladikavkaz 362027, Republic Of Nor, Russia

[2] RAS, Vladikavkaz Sci Ctr, Southern Math Inst, Dept Funct Anal, Vladikavkaz, Russia

关键词: Complex structure;    Universally complete vector lattice d-basis;    Band preserving operator;    Disjointness preserving operator;    Locally one-dimensional vector lattice;   

DOI  :  10.1016/j.jmaa.2016.03.040

来源: Elsevier

【 摘 要 】

The main result of this paper states that a universally complete real vector lattice admits a band preserving complex structure if and only if it contains no locally one-dimensional bands. A description of order bounded disjointness preserving complex structures on Archimedean semiprime f-algebras is also given. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free