Turkish Journal of Mathematics
Abstract
We show that compactness of orthogonally additive operators between Banach lattices is not preserved under taking the modulus by providing a nonlinear analogue of Krengel’s example. In contrast, for operators acting from a Banach lattice into an AM-space, AM-compactness is stable under lattice operations. Moreover, the space of absolutely norm bounded AM-compactorthogonally additive operators from a Banach lattice into an AM-space is a Banach lattice, and on such AM-spaces with the weak Fatou property, norm boundedness coincides with absolute norm boundedness.
DOI
10.55730/1300-0098.3782
Keywords
Riesz space, Banach lattice, orthogonally additive operator, compact orthogonally additive operator, AM-compact orthogonally additive operator
First Page
1067
Last Page
1076
Publisher
The Scientific and Technological Research Council of Türkiye (TÜBİTAK)
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
TURAN, B, & ALTIN, B (2026). Compact and AM-compact orthogonally additive operators. Turkish Journal of Mathematics 50 (5): 1067-1076. https://doi.org/10.55730/1300-0098.3782
