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Keywords:
Gelfand--Phillips property; Schur property; $p$-Schur property; weakly $p$-compact set; reciprocal Dunford--Pettis property of order $p$
Gelfand--Phillips property; Schur property; $p$-Schur property; weakly $p$-compact set; reciprocal Dunford--Pettis property of order $p$
Summary:
By using the concepts of limited $p$-converging operators between two Banach spaces $X$ and $Y$, $L_p$-sets and $L_p$-limited sets in Banach spaces, we obtain some characterizations of these concepts relative to some well-known geometric properties of Banach spaces, such as $*$-Dunford--Pettis property of order $p$ and Pelczyński's property of order $p$, $1\leq p<\infty$.
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