1. THE KADEC-PEŁCZYŃSKI THEOREM IN Lp, 1 ≤ p < 2.
- Author
-
BERKES, I. and TICHY, R.
- Subjects
VECTOR algebra ,VECTOR spaces ,MATHEMATICS theorems ,MATHEMATICS ,ALGEBRA - Abstract
By a classical result of Kadec and Pełczyński (1962), every normalized weakly null sequence in L
p , 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-Pełczyński theorem is that the limit random measure μ of the sequence satisfies ∫∨ x²dμ(x) ∈ Lp/2 . [ABSTRACT FROM AUTHOR]- Published
- 2016
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