Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

On the bundle convergence of double orthogonal series in noncommutative $L_2$-spaces

100%

Móricz F., Le Gac B.

Studia Mathematica

2000

tom 140

nr 2

177-190

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.

Bundle Convergence in a von Neumann Algebra and in a von Neumann Subalgebra

100%

Le Gac B., Móricz F.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

tom 52

nr 3

283-295

Let H be a separable complex Hilbert space, 𝓐 a von Neumann algebra in 𝓛(H), ϕ a faithful, normal state on 𝓐, and 𝓑 a commutative von Neumann subalgebra of 𝓐. Given a sequence (Xₙ: n ≥ 1) of operators in 𝓑, we examine the relations between bundle convergence in 𝓑 and bundle convergence in 𝓐.

Ograniczanie wyników

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 Studia Mathematica

2 Le Gac B.

2 Móricz F.

1 2004

1 2000

Wyniki wyszukiwania

On the bundle convergence of double orthogonal series in noncommutative $L_2$-spaces

Bundle Convergence in a von Neumann Algebra and in a von Neumann Subalgebra