A note on topologically b-order bounded sets and generalized b-weakly compact operators

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Hacettepe Journal of Mathematics and Statistics
Volume:51 Issue:2
A note on topologically b-order bounded sets and generalized b-weakly compact operators

A note on topologically b-order bounded sets and generalized b-weakly compact operators

Authors : Nabil MACHRAFI, Birol ALTIN

Pages : 483-493

Doi:10.15672/hujms.961727

View : 49 | Download : 13

Publication Date : 2022-04-01

Article Type : Research Paper

Abstract :We study the class of order weakly compact operators on locally solid Riesz spaces and the introduced class of generalized $b$-weakly compact operators on locally convex-solid Riesz spaces. We prove as a consequence that some well-known results on $b$-weakly compact operators on a Banach lattice extend in an improved version to generalized $b$-weakly compact operators on a Fréchet lattice.
Keywords : b order bounded set, order weakly compact operator, b weakly compact operator, locally convex solid Riesz space, Fréchet lattice, Banach lattice

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