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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