TY - JOUR AU - H. I. Humenchuk PY - 2015/12/25 Y2 - 2024/03/29 TI - On the sum of narrow and finite-rank orthogonally additive operators JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 67 IS - 12 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2095 AB - It is well known that the sum of two linear continuous narrow operators in the spaces Lp with 1 < p < ∞ need not be narrow. However, the sum of narrow and compact linear continuous operators is narrow. In a recent paper, M. Pliev and M. Popov started the investigation of nonlinear narrow operators and, in particular, of orthogonally additive operators. As our main result, we prove that the sum of a narrow orthogonally additive operator and a finite-rank laterally-to-normcontinuous orthogonally additive operator acting from an atomless Dedekind complete vector lattice into a Banach space is narrow. ER -