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.
Fields of Expertise
- Information, Communication & Computing
Treatment code (Nähere Zuordnung)
- Basic - Fundamental (Grundlagenforschung)