Abstract
We show that for the Köthe space X = c0 + 𝓁1(w), equipped with the Luxemburg norm, the set of norm attaining operators from X into any infinite-dimensional strictly convex Banach space Y is not dense in the space of all bounded operators. The same assertion holds for any infinite-dimensional L1(μ). This gives the first example of a classical space X satisfying the previous property. We also prove that all the spaces c0 + 𝓁1(w) are isomorphic for a large class of weights w.
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