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A Renorming of Nonreflexive Banach Spaces

1973
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Proceedings of the American Mathematical Society
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Every nonreflexive Banach space can be equivalently renormed in such a way that it is not isometrically a conjugate space. Dixmier [1] asked: "If A'is isomorphic to a conjugate Banach space, is X isometric to a conjugate space?" Klee [5] gave a negative solution by giving an equivalent norm for lx under which that space is not isometrically a dual space. Here, we show that such a norm exists for every nonreflexive Banach space. The result is precise since, obviously, if X is reflexive, it is

doi:10.2307/2039469
fatcat:pmeolwtftfbdhgvfn4tdwdpv5q