J. Aust. Math. Soc.
77 (2004), 357364

A dual differentiation space without an equivalent locally uniformly rotund norm

Petar S. Kenderov
Institute of Mathematics and Informatics
Bulgarian Academy of Sciences
Sofia
Bulgaria
kenderov@math.bas.bg





Abstract

A Banach space
is said to be a dual differentiation space
if every continuous convex function defined on a
nonempty 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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