Proximinality properties in Lp (μ,X) and polyhedral direct sums of Banach spaces
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چکیده
For a closed subspace Y of a Banach space X, we define a separably determined property for Y in X. Let (P) be either proximinality or strong 1 1 2 -ball property and if (P) is separably determined for Y in X, then we prove that L1(μ, Y ) has the same property (P) in L1(μ,X). For an M -embedded space X, we give a class of elements in L1(μ,X ∗∗) having best approximations from L1(μ,X). We also prove that some of these proximinality properties are stable under polyhedral direct sums of Banach spaces.
منابع مشابه
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تاریخ انتشار 2013