HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information

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

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.
Keywords :
Document type :
Journal articles

https://hal.archives-ouvertes.fr/hal-01281179
Contributor : Hermann Pfitzner Connect in order to contact the contributor
Submitted on : Tuesday, March 1, 2016 - 5:14:10 PM
Last modification on : Tuesday, October 12, 2021 - 5:20:13 PM

### Citation

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⟩

Record views