J. Aust. Math. Soc.
77 (2004), 357-364
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A dual differentiation space without an equivalent locally uniformly rotund norm
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Petar S. Kenderov
Institute of Mathematics and Informatics
Bulgarian Academy of Sciences
Sofia
Bulgaria
kenderov@math.bas.bg
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Abstract
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A Banach space
is said to be a dual differentiation space
if every continuous convex function defined on a
non-empty open convex subset
 of
 that possesses weak *
continuous subgradients at the points of a
residual subset of
 is Fréchet differentiable on a dense
subset of
 . In this paper we show that if we assume the
continuum hypothesis then there exists a dual
differentiation space that does not admit an
equivalent locally uniformly rotund norm.
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