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

Year 2022, Volume: 51 Issue: 2, 483 - 493, 01.04.2022

Nabil Machrafı , Birol Altın

https://doi.org/10.15672/hujms.961727

Cited By: 1

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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