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

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.