The Kadec–Pełczyński–Rosenthal subsequence splitting lemma for JBW$^∗$-triple preduals

Antonio M. Peralta (1) , H. Pfitzner (2)

1 Departamento de Analisis Matematico, Facultad de Ciencias
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

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.

Mots clés: Kadec–Pełczyński–Rosenthal subsequence splitting lemma; JBW$^*$-triples; weak compactness; uniform integrability; L-embedded Banach spaces

Domaines: Analyse fonctionnelle [math.FA]

Antonio M. Peralta, H. Pfitzner. The Kadec–Pełczyński–Rosenthal subsequence splitting lemma for JBW$^∗$-triple preduals. Studia Mathematica, 2015, 227 (1), pp.77-95. ⟨10.4064/sm227-1-5⟩. ⟨hal-01281179⟩