Algebraic structures on the set of narrow orthogonally additive operators

In this thesis, a research on the algebraic structures of the set of narrow orthogonally additive operators defined between a vector lattice and a normed space is given. Since multiplication of a narrow operator by a scalar is again narrow, the narrowness of the sum of two narrow operators is investigated . In this context, the examples of narrow orthogonally additive operators in which their sums are narrow were investigated. In the literature, several constructions on the two narrow operators or two narrow orthogonally additive operators whose sums are narrow are given. Some of these construction techniques belongs to H.I.Humenchuk, V.V.Mykhayluk with M.M.Popov and M.A.Pliev, F.Polat with M. R.Weber.