Abstract: We consider narrow linear operators defined on a Banach-Kantorovich space and taking value in a Banach space. We prove that the sum \(S+T\) of two operators is narrow whenever \(S\) is a narrow operator and \(T\) is a \((bo)\)-continuous \(C\)-compact operator. For the proof of the main result we use the method of decomposition of an element of a lattice-normed space into a sum of disjoint fragments and an approximation of a \(C\)-com\-pact operator by finite-rank operators.
For citation: Abasov N. M., Pliev M. A. On the Sum of Narrow and \(C\)-Compact Operators. Vladikavkazskij matematicheskij zhurnal [Vladikavkaz Math. J.], vol. 20, no. 1, pp.3-9. DOI 10.23671/VNC.2018.1.11391
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