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Summable families in nuclear groups

100%

Banaszczyk W.

Studia Mathematica

1993

tom 105

nr 3

271-282

Nuclear groups form a class of abelian topological groups which contains LCA groups and nuclear locally convex spaces, and is closed with respect to certain natural operations. In nuclear locally convex spaces, weakly summable families are strongly summable, and strongly summable are absolutely summable. It is shown that these theorems can be generalized in a natural way to nuclear groups.

The Lévy continuity theorem for nuclear groups

80%

Banaszczyk W.

Studia Mathematica

1999

tom 136

nr 2

183-196

Let G be an abelian topological group. The Lévy continuity theorem says that if G is an LCA group, then it has the following property (PL) a sequence of Radon probability measures on G is weakly convergent to a Radon probability measure μ if and only if the corresponding sequence of Fourier transforms is pointwise convergent to the Fourier transform of μ. Boulicaut [Bo] proved that every nuclear locally convex space G has the property (PL). In this paper we prove that the property (PL) is inherited by nuclear groups, a variety of abelian topological groups containing LCA groups and nuclear locally convex spaces, introduced in [B1].

Ograniczanie wyników

2 Studia Mathematica

2 Banaszczyk W.

1 1999

1 1993

Wyniki wyszukiwania

Summable families in nuclear groups

The Lévy continuity theorem for nuclear groups