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On unitary extensions and unitary completions of topological monoids

100%

Averbukh B. G.

Topological Algebra and its Applications

2016

tom 4

nr 1

The concept of a unitary Cauchy net in an arbitrary Hausdorff topological monoid generalizes the concept of a fundamental sequence of reals. We construct extensions of this monoid where all its unitary Cauchy nets converge.

On finest unitary extensions of topological monoids

100%

Averbukh B. G.

Topological Algebra and its Applications

2015

tom 3

nr 1

We prove that the Wyler completion of the unitary Cauchy space on a given Hausdorff topological 5 monoid consisting of the underlying set of this monoid and of the family of unitary Cauchy filters on it, is a T2-topological space and, in the commutative case, an abstract monoid containing the initial one.

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

63%

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.

Ograniczanie wyników

2 Topological Algebra and its Applications

1 Studia Mathematica

2 Averbukh B. G.

1 Le Gac B.

1 Móricz F.

1 2016

1 2015

1 2000

Wyniki wyszukiwania

On unitary extensions and unitary completions of topological monoids

On finest unitary extensions of topological monoids

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