On Bilinear Narrow Operators

Marat Pliev, Nonna Dzhusoeva and Ruslan Kulaev
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Marat Pliev: Southern Mathematical Institute, Russian Academy of Sciences, 362027 Vladikavkaz, Russia
Nonna Dzhusoeva: Department of Mathematics and Computer Sciences, North-Ossetian State University Named after K.L. Khetagurov, 362025 Vladikavkaz, Russia
Ruslan Kulaev: Southern Mathematical Institute, Russian Academy of Sciences, 362027 Vladikavkaz, Russia

Mathematics, 2021, vol. 9, issue 22, 1-12

Abstract: In this article, we introduce a new class of operators on the Cartesian product of vector lattices. We say that a bilinear operator T : E × F ? W defined on the Cartesian product of vector lattices E and F and taking values in a vector lattice W is narrow if the partial operators T x and T y are narrow for all x ? E , y ? F . We prove that, for order-continuous Köthe–Banach spaces E and F and a Banach space X , the classes of narrow and weakly function narrow bilinear operators from E × F to X are coincident. Then, we prove that every order-to-norm continuous C -compact bilinear regular operator T is narrow. Finally, we show that a regular bilinear operator T from the Cartesian product E × F of vector lattices E and F with the principal projection property to an order continuous Banach lattice G is narrow if and only if | T | is.

Keywords: bilinear operator; narrow operator; order-to-norm continuous operator; C -compact operator; regular operator; Köthe–Banach space; vector lattice (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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