Abstract
By a classical result of Kadec and Pelczynski (1962), every normalized weakly null sequence in Lp, p > 2 contains a subsequence equivalent to the unit vector basis of ℓ2 or to the unit vector basis of ℓp. 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 x2dμ(x) ∈ Lp/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)