Abstract
A linear metric space (X, d) is called a convex linear metric space if for all x, y in X, it also satisfies \(d(\lambda x+(1-\lambda )y,0)\le \lambda d(x,0)+(1-\lambda )d(y,0)\) whenever \(0\le \lambda \le 1\). Such spaces, known to be more general than normed linear spaces, are examples of convex metric spaces extensively discussed in the literature. In this article, we show that convex linear metric spaces are infact normable.
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The authors are thankful to the learned referee for valuable comments and suggestions leading to an improvement of the paper.
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Singh, J., Narang, T.D. Convex linear metric spaces are normable. J Anal 28, 705–709 (2020). https://doi.org/10.1007/s41478-019-00185-1
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DOI: https://doi.org/10.1007/s41478-019-00185-1