COMPLEMENTED COPIES OF l1 IN SPACES OF VECTOR MEASURES AND APPLICATIONS
نویسنده
چکیده
Let X be a Banach space and (Ω,Σ) be a measure space. We provide a characterization of sequences in the space of X-valued countably additive measures on (Ω,Σ) of bounded variation that generates complemented copies of l1. As application, we prove that if a dual Banach space E∗ has Pe lczyński’s property (V*) then so does the space of E∗-valued countably additive measures with the variation norm. Another application, we show that for a Banach space X , the space l∞(X) contains a complemented copy of l1 if and only if X contains all l n 1 uniformly complemented.
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