The Kadec–Pełczyński–Rosenthal subsequence splitting lemma for JBW$^*$-triple preduals
Volume 227 / 2015
Studia Mathematica 227 (2015), 77-95
MSC: Primary 17C65, 46L70, 46B08; Secondary 46B04, 46L51.
DOI: 10.4064/sm227-1-5
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.
