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

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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