Geodesic
Using boundaries to find smooth norms
Victor Bible 1
1 UCD School of Mathematical Sciences Belfield, Dublin 4, Ireland
Studia Mathematica, Tome 224 (2014) no. 2, pp. 169-181 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm224-2-5
Keywords: paper present tool certain banach spaces endowed smooth equivalent norms hypothesis uses particular countable decompositions certain subsets * namely boundaries interest main result unifies quite known results final section corollaries given

Victor Bible  1

1 UCD School of Mathematical Sciences Belfield, Dublin 4, Ireland 
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Victor Bible. Using boundaries to find smooth norms. Studia Mathematica, Tome 224 (2014) no. 2, pp. 169-181. doi: 10.4064/sm224-2-5

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