Back to Search
Start Over
Representation theorems for regular operators.
- Source :
-
Mathematische Nachrichten . Jan2024, Vol. 297 Issue 1, p126-143. 18p. - Publication Year :
- 2024
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *BANACH lattices
*RIESZ spaces
*LINEAR operators
Subjects
Details
- Language :
- English
- ISSN :
- 0025584X
- Volume :
- 297
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Mathematische Nachrichten
- Publication Type :
- Academic Journal
- Accession number :
- 174779621
- Full Text :
- https://doi.org/10.1002/mana.202200129