Czechoslovak Mathematical Journal

, Volume 67, Issue 2, pp 457–467

Copies of lpn’s uniformly in the spaces Π2(C[0, 1],X) and Π1(C[0, 1],X)

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Abstract

We study the presence of copies of lpn’s uniformly in the spaces Π2(C[0, 1],X) and Π1(C[0, 1],X). By using Dvoretzky’s theorem we deduce that if X is an infinite-dimensional Banach space, then Π2(C[0, 1],X) contains \(\lambda \sqrt 2 \) -uniformly copies of ln’s and Π1(C[0, 1],X) contains λ-uniformly copies of l2n’s for all λ > 1. As an application, we show that if X is an infinite-dimensional Banach space then the spaces Π2(C[0, 1],X) and Π1(C[0, 1],X) are distinct, extending the well-known result that the spaces Π2(C[0, 1],X) and N(C[0, 1],X) are distinct.

Keywords

p-summing linear operators copies of lpn’s uniformly local structure of a Banach space multiplication operator average 

MSC 2010

46B07 47B10 47L20 46B28 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  1. 1.Department of MathematicsOvidius University of ConstanţaConstanţaRomania

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