In this paper, for an isometric strongly continuous linear representation
denoted by ? of the topological group of the unit circle in complex Banach
space, we study an integral representation for Abel-Poisson mean A?r (x)
of the Fourier coefficients family of an element x, and it is proved that this
family is Abel-Poisson summable to x. Finally, we give some tests which are
related to characterizations of relatively compactness of a subset by means
of Abel-Poisson operator A?r and ?.
AbstractThe paper deals with the questions: (a)whether a topological module admits maximal linearly independent subsets that are analytic(b)whether an Abelian topological group admits maximal independent subsets that are analytic(c)whether a topological field extension admits transcendence bases that are analytic.
AbstractWe give some general results concerning continuity of measurable homomorphisms of topological groups. As a consequence we show that a Christensen measurable homomorphism of a Polish abelian group into a locally compact topological group is continuous. We also obtain similar results for the universally measurable homomorphisms and the homomorphisms that have the Baire property.
On a characterization of compactness and the Abel-Poisson summability of fourier coefficients in Banach spaces
