EXTENSION OF LUR NORM TO FRECHET DIFFERENTIALBE NORM
DOI:
https://doi.org/10.3126/jist.v31i1.83026Keywords:
Strictly Convexity, Locally Uniform Rotund, Frechet Differentiable Norm, Reflexive Space, Separable SpacesAbstract
In this paper, we discuss the extension of norms possessing rotundity properties from a closed, reflexive, and separable subspace of a Banach space to the entire space. We also explore the possibility of extending an equivalent Fréchet differentiable norm defined on a subspace of a reflexive and separable Banach space to an equivalent norm on the whole space, such that the corresponding dual norm is locally uniformly rotund (LUR). This is an open problem in general.
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