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arXiv · 1311.1408

Using boundaries to find smooth norms

Victor Bible
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Abstract

The aim of this paper is to present a tool used to show that certain Banach spaces can be endowed with $C^k$ smooth equivalent norms. The hypothesis uses particular countable decompositions of certain subsets of $B_{X^*}$, namely boundaries. Of interest is that the main result unifies two quite well known results. In the final section, some new corollaries are given.

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Victor Bible. 2014-04-28. Using boundaries to find smooth norms. https://doi.org/10.4064/sm224-2-5

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