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DOI: 10.23671/VNC.2018.1.11391

On the Sum of Narrow and \(C\)-Compact Operators

Abasov N. M. , Pliev, M. A.
Vladikavkaz Mathematical Journal 2018. Vol. 20. Issue 1.
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.
Keywords: Banach space, Banach-Kantorovich space, narrow operator, \((bo)\)-continuous operator, \(C\)-compact operator
Language: Russian Download the full text  
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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