$C^k$-smooth approximations of LUR norms
PROCHAZKA, Antonin
Institut de Mathématiques de Bordeaux [IMB]
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
Institut de Mathématiques de Bordeaux [IMB]
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
PROCHAZKA, Antonin
Institut de Mathématiques de Bordeaux [IMB]
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
< Reduce
Institut de Mathématiques de Bordeaux [IMB]
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
Language
en
Article de revue
This item was published in
Transactions of the American Mathematical Society. 2014, vol. 366, p. 1973-1992
American Mathematical Society
English Abstract
Let $X$ be a WCG Banach space admitting a $C^k$-Fr\' echet smooth norm. Then $X$ admits an equivalent norm which is simultaneously $C^1$-Fr\' echet smooth, LUR, and a uniform limit of $C^k$-Fr\' echet smooth norms. If ...Read more >
Let $X$ be a WCG Banach space admitting a $C^k$-Fr\' echet smooth norm. Then $X$ admits an equivalent norm which is simultaneously $C^1$-Fr\' echet smooth, LUR, and a uniform limit of $C^k$-Fr\' echet smooth norms. If $X=C([0,\alpha])$, where $\alpha$ is an ordinal, then the same conclusion holds true with $k=\infty$.Read less <
English Keywords
LUR
higher order differentiability
renorming
Origin
Hal imported