Geodesic
On the bundle convergence of double orthogonal series in noncommutative $L_2$-spaces
Studia Mathematica, Tome 140 (2000) no. 2, pp. 177-190

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The notion of bundle convergence in von Neumann algebras and their $L_2$-spaces for single (ordinary) sequences was introduced by Hensz, Jajte, and Paszkiewicz in 1996. Bundle convergence is stronger than almost sure convergence in von Neumann algebras. Our main result is the extension of the two-parameter Rademacher-Men'shov theorem from the classical commutative case to the noncommutative case. To our best knowledge, this is the first attempt to adopt the notion of bundle convergence to multiple series. Our method of proof is different from the classical one, because of the lack of the triangle inequality in a noncommutative von Neumann algebra. In this context, bundle convergence resembles the regular convergence introduced by Hardy in the classical case. The noncommutative counterpart of convergence in Pringsheim's sense remains to be found.
DOI : 10.4064/sm-140-2-177-190
Keywords: von Neumann algebra, faithful and normal state, completion, Gelfand-Naimark-Segal representation theorem, bundle convergence, almost sure convergence, regular convergence, orthogonal sequence of vectors in $L_2$, Rademacher-Men'shov theorem, convergence in Pringsheim's sense

Ferenc Móricz 1 ; Barthélemy Le Gac 1

1 
@article{10_4064_sm_140_2_177_190,
     author = {Ferenc M\'oricz and Barth\'elemy Le Gac},
     title = {On the bundle convergence of double orthogonal series in noncommutative $L_2$-spaces},
     journal = {Studia Mathematica},
     pages = {177--190},
     publisher = {mathdoc},
     volume = {140},
     number = {2},
     year = {2000},
     doi = {10.4064/sm-140-2-177-190},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-140-2-177-190/}
}
TY  - JOUR
AU  - Ferenc Móricz
AU  - Barthélemy Le Gac
TI  - On the bundle convergence of double orthogonal series in noncommutative $L_2$-spaces
JO  - Studia Mathematica
PY  - 2000
SP  - 177
EP  - 190
VL  - 140
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm-140-2-177-190/
DO  - 10.4064/sm-140-2-177-190
LA  - en
ID  - 10_4064_sm_140_2_177_190
ER  - 
%0 Journal Article
%A Ferenc Móricz
%A Barthélemy Le Gac
%T On the bundle convergence of double orthogonal series in noncommutative $L_2$-spaces
%J Studia Mathematica
%D 2000
%P 177-190
%V 140
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm-140-2-177-190/
%R 10.4064/sm-140-2-177-190
%G en
%F 10_4064_sm_140_2_177_190
Ferenc Móricz; Barthélemy Le Gac. On the bundle convergence of double orthogonal series in noncommutative $L_2$-spaces. Studia Mathematica, Tome 140 (2000) no. 2, pp. 177-190. doi: 10.4064/sm-140-2-177-190

Cité par Sources :