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Gelfand Numbers and Euclidean Sections of Large Dimensions

  • Alain Pajor
  • Nicole Tomczak-Jaegermann
Part of the Progress in Probability book series (PRPR, volume 20)

Abstract

Let E = (ℝ n , ‖.‖) be an n-dimensional Banach space and let B E be the unit ball in E. We shall also consider a Euclidean structure on ℝ n , and so, let (·,·) denote an inner product and ‖.2 the corresponding Euclidean norm. The dual space E * is naturally identified to (ℝ n , ‖.*), where
$$\parallel x\parallel =\sup \left\{ \left| \left( x,y \right) \right|\left| y\in {{B}_{E}} \right. \right\}.$$
(1)

Keywords

Banach Space Euclidean Norm Universal Constant Euclidean Ball Entropy Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 1990

Authors and Affiliations

  • Alain Pajor
    • 1
  • Nicole Tomczak-Jaegermann
    • 2
  1. 1.U.E.R. de MathematiquesUniversité des Sciences et Techniques de LilleVillaneuve d’AscqFrance
  2. 2.Department of MathematicsUniversity of AlbertaEdmonton, AlbertaCanada

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