Separated sequences in asymptotically uniformly convex Banach spaces

Volume 119 / 2010

Sylvain Delpech Colloquium Mathematicum 119 (2010), 123-125 MSC: Primary 46B20. DOI: 10.4064/cm119-1-7


We prove that the unit sphere of every infinite-dimensional Banach space $X$ contains an $\alpha $-separated sequence, for every $0<\alpha <1+ \overline {\delta }_X(1)$, where $\overline {\delta }_X$ denotes the modulus of asymptotic uniform convexity of $X$.


  • Sylvain Delpech26 bis rue Xavier Privas
    69008 Lyon, France

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