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Autor
- Berkes, István
- Tichy, Robert
TitelThe Kadec-Pelczynski theorem in $L^p$ , $1 ≤ p 2$
Datei
- [107.78 KB]
DOI10.1090/proc/12872
Erschienen inProceedings of the American Mathematical Society
Band144
Erscheinungsjahr2016
Heft5
Seiten2053-2066
LicenceCC BY
ISSN1088-6826
Zugriffsrechte
Download Statistik73
Peer ReviewJa
AbstractBy a classical result of Kadec and Pe lczynski (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 $∫_{\mathbb{R}} x^2 dμ(x) ∈ L^{p/2}$ .

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