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- Title
Orthogonally Bi-additive Operators-II.
- Authors
Dzhusoeva, Nonna; Mazloeva, Madina
- Abstract
In this paper, we extend to the setting of positive orthogonally bi-additive operators several results from Aliprantis and Burkinshaw (Math Z 185: 245-257, 1983), de Pagter (Math Anal Appl 472: 238-245, 2019), Pliev and Popov (Siberian Math J 57: 552-557, 2016), Pliev and Ramdane (Mediter J Math 15(2): 55, 2018). First, we show that a positive order bounded orthogonally bi-additive map T : I → W defined on a lateral ideal of a Cartesian product of vector lattices E and F and taking values in a Dedekind complete vector lattice W can be extended to the whole space E × F . Then we prove that a positive orthogonally bi-additive operator T : E × F → W is laterally-to-order continuous if and only if the kernel of each S with 0 ≤ S ≤ T is laterally closed. Finally, we calculate the laterally-to-order continuous part of a positive orthogonally bi-additive operator T : E × F → W .
- Subjects
RIESZ spaces; BANACH lattices; POSITIVE operators; MATHEMATICS
- Publication
Results in Mathematics / Resultate der Mathematik, 2023, Vol 78, Issue 5, p1
- ISSN
1422-6383
- Publication type
Article
- DOI
10.1007/s00025-023-01957-9