We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Representation theorems for regular operators.
- Authors
Pliev, Marat; Popov, Mikhail
- 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.
- Subjects
BANACH lattices; RIESZ spaces; LINEAR operators
- Publication
Mathematische Nachrichten, 2024, Vol 297, Issue 1, p126
- ISSN
0025-584X
- Publication type
Article
- DOI
10.1002/mana.202200129