## Abstract

By a classical result of Kadec and Pelczynski (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 ∫_{ℝ}*x*∈^{2}dμ(x)*L*

^{p/2}.Original language | English |
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Pages (from-to) | 2053-2066 |

Number of pages | 14 |

Journal | Proceedings of the American Mathematical Society |

Volume | 144 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2016 |

## Fields of Expertise

- Information, Communication & Computing

## Treatment code (Nähere Zuordnung)

- Basic - Fundamental (Grundlagenforschung)

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