Representation theorems for regular operators

Marat Pliev and Mikhail Popov

Mathematische Nachrichten, 2024, vol. 297, issue 1, 126-143

Abstract: We elaborate, strengthen, and generalize known representation theorems by different authors for regular operators on vector and Banach lattices. Our main result asserts, in particular, that every regular linear operator T acting from a vector lattice E with the principal projection property to a Dedekind complete vector lattice F, which is an ideal of some order continuous Banach lattice G, admits a unique representation T=Ta+Tc$T = T_a + T_c$, where Ta$T_a$ is the sum of an absolutely order summable family of disjointness preserving operators and Tc$T_c$ is an order narrow (= diffuse) operator. Our main contribution is waiver of the order continuity assumption on T. In proofs, we use new techniques that allow obtaining more general results for a wider class of orthogonally additive operators, which has somewhat different order structure than the linear subspace of linear operators.

Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.202200129

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:297:y:2024:i:1:p:126-143

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().