### wMB-Property of Order $p$ in Banach Spaces

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**Authors:**MANIJEH BAHREINI ESFAWHANI

**DOI:**10.46793/KgJMat2201.029E

**Abstract:**

In this paper, we introduce a new property of Banach spaces called wMB-property of order p (1 ≤ p < ∞). 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.

**Keywords:**

p-Convergent operators, weakly-p-L-sets, Dunford-Pettis property of order p.

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