Abstract
We prove that ifEis a Dedekind complete atomless Riesz space andXis a Banach space, then the sum of two laterally continuous orthogonally additive operators fromEtoX, one of which is strictly narrow and the other one is hereditarily strictly narrow with finite variation (in particular, has finite rank), is strictly narrow. Similar results were previously obtained for narrow operators by different authors; however, no theorem of the kind was known for strictly narrow operators.
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