The present paper completes investigation [2] of the first named author. Theorem 3.1 of the cited paper asserting that the sum of a narrow and a finite rank orthogonally additive operator is narrow, is proved under assumptions on the domain vector lattice that fail for the wide class of K¨othe spaces on an atomless measure space. Using the technique and the idea of proof of the theorem from [2] we establish new assumptions on the domain vector lattice under which the theorem holds true, and prove that lots of vector lattices satisfy these assumptions, in particular, K¨othe spaces on an atomless measure space.
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- ACS Style
- Gumenchuk, H.; Popov, M.M. On the sum of narrow and finite-dimensional operators on vector lattices. Bukovinian Mathematical Journal. 2017, 5
- AMA Style
- Gumenchuk H, Popov MM. On the sum of narrow and finite-dimensional operators on vector lattices. Bukovinian Mathematical Journal. 2017; 5(1-2).
- Chicago/Turabian Style
- Hanna Gumenchuk, Mykhailo Mykhailovych Popov. 2017. "On the sum of narrow and finite-dimensional operators on vector lattices". Bukovinian Mathematical Journal. 5 no. 1-2.