Types et suites symétriques dans \(L^ p\), \(1\leq p<+\infty\), p\(\neq 2\). (Types and symmetric sequences in \(L^ p\), \(1\leq p<+\infty\), p\(\neq 2)\)
We prove that every normalized sequence in \(L^ p\), weakly null if \(p>2\) and equivalent to the unit vector basis of \(\ell^ 2\) if \(1\leq p<2\), has for all \(\epsilon >0\) a subsequence which is \(2(1+\epsilon)\)-symmetric. This result was known for \(p=1\) (H. P. Rosenthal) and \(p\in 2{\mathbb{N}}\) (W. B. Johnson, B. Maurey, G. Shechtman, L. Tzafriri). Here, we use the techniques of stability which were introduced by J. L. Krivine and B. Maurey: as well as providing new results, this approach unifies and simplifies previous known results.
scientific article; zbMATH DE number 3955709