UO - Université d'Orléans : UMR 7349 (Château de la Source - Avenue du Parc Floral - BP 6749 - 45067 Orléans cedex 2 - France)
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.
Antonio Peralta, H. Pfitzner. The Kadec–Pełczyński–Rosenthal subsequence splitting lemma for JBW$^∗$-triple preduals. Studia Mathematica, Instytut Matematyczny - Polska Akademii Nauk, 2015, 227 (1), pp.77-95. ⟨10.4064/sm227-1-5⟩. ⟨hal-01281179⟩