Full length article: Gelfand numbers and widths

  • Authors:

  • David E. Edmunds;Jan Lang

  • Affiliations:

  • Department of Mathematics, University of Sussex, Pevensey I, Brighton, BN1 9QH, United Kingdom;Department of Mathematics, The Ohio State University, 100 Math Tower, 231 West 18th Avenue, Columbus, OH43210-1174, USA

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2013

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Abstract

In general, the Gelfand widths c@?"n(T) of a map T between Banach spaces X and Y are not equivalent to the Gelfand numbers c"n(T) of T. We show that c@?"n(T)=c"n(T)(n@?N) provided that X and Y are uniformly convex and uniformly smooth, and T has trivial kernel and dense range.