Abstract
W. Freedman introduced an alternate to the Dunford‐Pettis property, called the DP1 property, in 1997. He showed that for 1 ≤ p < ∞, has the DP1 property if and only if each Xα does. This is not the case for . In fact, we show that has the DP1 property if and only if it has the Dunford‐Pettis property. A similar result also holds for vector‐valued continuous function spaces.
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