Any bounded sequence in an L¹-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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm227-1-5,
author = {Antonio M. Peralta and Hermann Pfitzner},
title = {The Kadec-Pe\l czy\'nski-Rosenthal subsequence splitting lemma for JBW*-triple preduals},
journal = {Studia Mathematica},
volume = {231},
year = {2015},
pages = {77-95},
zbl = {06446128},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm227-1-5}
}
Antonio M. Peralta; Hermann Pfitzner. The Kadec-Pełczyński-Rosenthal subsequence splitting lemma for JBW*-triple preduals. Studia Mathematica, Tome 231 (2015) pp. 77-95. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm227-1-5/