Abstract : Any bounded sequence in an $L^1$-space admits a subsequence which can be written as the sum of a sequence of pairwise disjoint elements and a sequence which forms a uniformly integrable or equiintegrable (equivalently, a relatively weakly compact) set. This is known as the Kadec–Pełczyński–Rosenthal subsequence splitting lemma and has been generalized to preduals of von Neuman algebras and of JBW∗-algebras. In this note we generalize it to JBW$^∗$-triple preduals.
https://hal.archives-ouvertes.fr/hal-01281179
Contributeur : Hermann Pfitzner
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Soumis le : mardi 1 mars 2016 - 17:14:10
Dernière modification le : jeudi 3 mai 2018 - 15:32:07
Antonio Peralta, H. Pfitzner. The Kadec–Pełczyński–Rosenthal subsequence splitting lemma for JBW$^∗$-triple preduals. Studia Mathematica, INSTYTUT MATEMATYCZNY * POLSKA AKADEMIA NAUK, 2015, 227 (1), pp.77-95. 〈10.4064/sm227-1-5 〉. 〈hal-01281179〉
