1Departamento de Análisis Matemático Universidad de Granada Facultad de Ciencias 18071 Granada, Spain Current address: Department of Mathematics College of Science King Saud University P.O. Box 2455-5 Riyadh 11451, Kingdom of Saudi Arabia 2Université d'Orléans BP 6759 F-45067 Orléans Cedex 2, France
Studia Mathematica, Tome 227 (2015) no. 1, pp. 77-95
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 :
bounded sequence space admits subsequence which written sum sequence pairwise disjoint elements sequence which forms uniformly integrable equiintegrable equivalently relatively weakly compact set known kadec czy ski rosenthal subsequence splitting lemma has generalized preduals von neuman algebras jbw * algebras note generalize jbw * triple preduals
Affiliations des auteurs :
Antonio M. Peralta
1
;
Hermann Pfitzner
2
1
Departamento de Análisis Matemático Universidad de Granada Facultad de Ciencias 18071 Granada, Spain Current address: Department of Mathematics College of Science King Saud University P.O. Box 2455-5 Riyadh 11451, Kingdom of Saudi Arabia
2
Université d'Orléans BP 6759 F-45067 Orléans Cedex 2, France
@article{10_4064_sm227_1_5,
author = {Antonio M. Peralta and Hermann Pfitzner},
title = {The {Kadec{\textendash}Pe{\l}czy\'nski{\textendash}Rosenthal} subsequence splitting lemma for {JBW}$^*$-triple preduals},
journal = {Studia Mathematica},
pages = {77--95},
year = {2015},
volume = {227},
number = {1},
doi = {10.4064/sm227-1-5},
language = {pl},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm227-1-5/}
}
TY - JOUR
AU - Antonio M. Peralta
AU - Hermann Pfitzner
TI - The Kadec–Pełczyński–Rosenthal subsequence splitting lemma for JBW$^*$-triple preduals
JO - Studia Mathematica
PY - 2015
SP - 77
EP - 95
VL - 227
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4064/sm227-1-5/
DO - 10.4064/sm227-1-5
LA - pl
ID - 10_4064_sm227_1_5
ER -
%0 Journal Article
%A Antonio M. Peralta
%A Hermann Pfitzner
%T The Kadec–Pełczyński–Rosenthal subsequence splitting lemma for JBW$^*$-triple preduals
%J Studia Mathematica
%D 2015
%P 77-95
%V 227
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/sm227-1-5/
%R 10.4064/sm227-1-5
%G pl
%F 10_4064_sm227_1_5
Antonio M. Peralta; Hermann Pfitzner. The Kadec–Pełczyński–Rosenthal subsequence splitting lemma for JBW$^*$-triple preduals. Studia Mathematica, Tome 227 (2015) no. 1, pp. 77-95. doi: 10.4064/sm227-1-5
