Abstract
We prove that every normalized sequence inL p, weakly null ifp>2 and equivalent to the unit vector basis ofl 2 if 1≦p<2, has for allε>0 a subsequence which is 2(1+ε)-symmetric. This result was known forp=1 (H.P. Rosenthal) andp∈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.
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Guerre, S. Types et suites symetriques dansL p, 1≦p<+∞,p≠2. Israel J. Math. 53, 191–208 (1986). https://doi.org/10.1007/BF02772858
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DOI: https://doi.org/10.1007/BF02772858