structural engineering and mechanics2003Vol. 2003pp. 2375-2378
57
bator2003internationaldp1
Abstract
W. Freedman introduced an alternate to the
Dunford-Pettis property, called the DP1 property,
in 1997. He showed that for 1≤p<∞,
(⊕α∈𝒜Xα)p has the DP1 property if and only if each Xα does. This is not the case for (⊕α∈𝒜Xα)∞. In
fact, we show that (⊕α∈𝒜Xα)∞ 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.