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  • Autor
    • Berkes, István
    • Tichy, Robert
  • TitelThe Kadec-Pelczynski theorem in \(L^p\) , \(1 ≤ p 2\)
  • Volltext
  • DOI10.1090/proc/12872
  • Erschienen inProceedings of the American Mathematical Society
  • Band144
  • Erscheinungsjahr2016
  • Heft5
  • Seiten2053-2066
  • LicenceCC BY
  • ISSN1088-6826
  • ZugriffsrechteCC-BY
  • Download Statistik10
  • Peer ReviewJa
  • AbstractBy a classical result of Kadec and Pe lczynski (1962), every normalized weakly null sequence in \(L^p\) , \(p > 2\) contains a subsequence equivalent to the unit vector basis of \(l^2\) or to the unit vector basis of \(l^p\) . In this paper we investigate the case \(1 ≤ p < 2\) and show that a necessary and sufficient condition for the first alternative in the Kadec-Pelczynski theorem is that the limit random measure μ of the sequence satisfies \(∫_{\mathbb{R}} x^2 dμ(x) ∈ L^{p/2}\) .