- Tytuł:
- On the bundle convergence of double orthogonal series in noncommutative $L_2$-spaces
- Autorzy:
-
Móricz, Ferenc
Le Gac, Barthélemy - Powiązania:
- https://bibliotekanauki.pl/articles/1206079.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
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 - Opis:
- 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.
- Źródło:
-
Studia Mathematica; 2000, 140, 2; 177-190
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł