Abstract
We study the b-weakly compact operators using the Banach-Saks sets. More precisely, we will establish that an operator T from a Banach lattice E into a Banach space Y is b-weakly compact if and only if T carries b-order bounded subsets of E onto Banach-Saks subsets of Y. Next we give a sequential characterization of these operators without requiring the sequences to be disjoint. Also, we describe the relationships between b-weakly compact, and b-L-weakly compact operators.
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Baklouti, H., Hajji, M. & Moulahi, R. On the class of b-weakly compact operators. Positivity 26, 7 (2022). https://doi.org/10.1007/s11117-022-00892-3
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DOI: https://doi.org/10.1007/s11117-022-00892-3