Geodesic
The strong Dunford-Pettis relatively compact property of order p
Filomat, Tome 37 (2023) no. 22, p. 7339

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DOI

We introduce and study Banach lattices with the strong Dunford-Pettis relatively compact property of order p (1 ≤ p ∞); that is, spaces in which every weakly p-compact and almost Dunford-Pettis set is relatively compact. We also introduce the notion of the weak Dunford-Pettis property of order p and then characterize this property in terms of sequences. In particular, in terms of disjoint weakly compact operators into c 0 , an operator characterization of those Banach lattices with the weak Dunford-Pettis property of order p is given. Moreover, some results about Banach lattices with the positive Dunford-Pettis relatively compact property of order p are presented.
DOI : 10.2298/FIL2322339A
Classification : 46B42, 46B50, 47B65
Keywords: Almost Dunford-Pettis set, Weak Dunford-Pettis property, Dunford-Pettis relatively compact property, Weakly p- summable sequence, p-convergent operator 
Halimeh Ardakani; Khadijeh Taghavinejad; Sharifeh Rezagholi. The strong Dunford-Pettis relatively compact property of order p. Filomat, Tome 37 (2023) no. 22, p. 7339 . doi: 10.2298/FIL2322339A
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     author = {Halimeh Ardakani and Khadijeh Taghavinejad and Sharifeh Rezagholi},
     title = {The strong {Dunford-Pettis} relatively compact property of order p},
     journal = {Filomat},
     pages = {7339 },
     year = {2023},
     volume = {37},
     number = {22},
     doi = {10.2298/FIL2322339A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2322339A/}
}
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