1. THE KADEC-PEŁCZYŃSKI THEOREM IN Lp, 1 ≤ p < 2.
- Author
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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 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-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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