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Two Remarks on 1-Unconditional Basic Sequences in Lp, 3 ≤ p < ∞

  • Gideon Schechtman
Conference paper
Part of the Operator Theory Advances and Applications book series (OT, volume 77)

Abstract

We recall that the p-concavity constant of a Banach lattice L is the smallest constant C for which the inequality
$$ {\left( {{{\sum\limits_{i = 1}^n {\left\| {{x_i}} \right\|} }^p}} \right)^{1/p}} \leqslant C\left\| {{{\left( {\sum\limits_{i = 1}^n {{{\left| {{x_i}} \right|}^p}} } \right)}^{1/p}}} \right\| $$
holds for all n and all x 1, x 2,…,x n L. Here 1 ≤ p < ∞. The p-convexity constant is defined similarly. We refer the reader to [LT II] for more information on these notions.

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References

  1. [LT II]
    Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces II, Function spaces, Springer-Verlag, Berlin (1979).zbMATHGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 1995

Authors and Affiliations

  • Gideon Schechtman
    • 1
  1. 1.The Weizmann InstituteRehovotIsrael

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