Geodesic
$wMB$-Property of Order $p$ in Banach Spaces
Kragujevac Journal of Mathematics, Tome 46 (2022) no. 1, p. 29 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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In this paper, we introduce a new property of Banach spaces called $wMB$-property of order $p$ ($1 \leq p \infty$). A necessary and sufficient condition for a Banach space to have the $wMB$-property of order $p$ is given. We study $p$-convergent operators and weakly-$p$-$L$-sets. Banach spaces with the $wMB$-property of order $p$ are characterized. Also, the Dunford-Pettis property of order $p$ and $DP^*$-property of order $p$ are studied in Banach spaces. Finally we show the relation between Pelczynski's property $(V)$ and $wMB$-property of order $p$.
Classification : 46B20, 46B25, 46B28
Keywords: p-convergent operators, weakly-p-L-sets, Dunford-Pettis property of order p 
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     author = {Manijeh Bahreini Esfahani},
     title = {$wMB${-Property} of {Order} $p$ in {Banach} {Spaces}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {29 },
     year = {2022},
     volume = {46},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2022_46_1_a2/}
}
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Manijeh Bahreini Esfahani. $wMB$-Property of Order $p$ in Banach Spaces. Kragujevac Journal of Mathematics, Tome 46 (2022) no. 1, p. 29 . http://geodesic.mathdoc.fr/item/KJM_2022_46_1_a2/