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.
b-order bounded set order weakly compact operator b-weakly compact operator locally convex-solid Riesz space Fréchet lattice Banach lattice.
Primary Language | English |
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Subjects | Mathematical Sciences |
Journal Section | Mathematics |
Authors | |
Publication Date | April 1, 2022 |
Published in Issue | Year 2022 Volume: 51 Issue: 2 |