论文信息 - Gelfand Numbers and Euclidean Sections of Large Dimensions

Gelfand Numbers and Euclidean Sections of Large Dimensions

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)

Alain Pajor | Nicole Tomczak-Jaegermann

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