Gelfand Numbers and Euclidean Sections of Large Dimensions

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


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
$$\parallel x\parallel =\sup \left\{ \left| \left( x,y \right) \right|\left| y\in {{B}_{E}} \right. \right\}.$$


Banach Space Euclidean Norm Universal Constant Euclidean Ball Entropy Number 
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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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