- Autor
- Berkes, István
- Tichy, Robert
- TitelThe Kadec-Pelczynski theorem in \(L^p\) , \(1 ≤ p 2\)
- Datei
- DOI10.1090/proc/12872
- Erschienen inProceedings of the American Mathematical Society
- Band144
- Erscheinungsjahr2016
- Heft5
- Seiten2053-2066
- LicenceCC BY
- ISSN1088-6826
- Download Statistik1526
- 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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