Abstract
In this paper, our central focus is upon introducing the class of demi Dunford–Pettis operators. The paper rests essentially on two parts. In the first part we study the connection of this new class of operators with classical notions of operators, such as Dunfort–Pettis operators, strictly singular operators and demicompact operators. In the second part we characterize Banach lattices for which each demi Dunford–Pettis operator is M-weakly demicompact (resp. L-weakly demicompact).
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Benkhaled, H., Hajji, M. & Jeribi, A. On the class of demi Dunford–Pettis operators. Rend. Circ. Mat. Palermo, II. Ser 72, 901–911 (2023). https://doi.org/10.1007/s12215-021-00702-x
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DOI: https://doi.org/10.1007/s12215-021-00702-x
Keywords
- Demi Dunford–Pettis operator
- L-weakly demicompact operator
- M-weakly demicompact operator
- Schur property
- Banach lattice
- Order continuous norm
- Discrete vector lattice