A note on rational approximation with respect to metrizable compactifications of the plane

In the present note we examine possible extensions of Runge, Mergelyan and Arakelian Theorems, when the uniform approximation is meant with respect to the metric ϱ of a metrizable compactification (S, ϱ) of the complex plane C.peerReviewe

A note on rational approximation with respect to metrizable compactifications of the plane

In the present note we examine possible extensions of Runge, Mergelyan and Arakelian Theorems, when the uniform approximation is meant with respect to the metric ϱ of a metrizable compactification (S, ϱ) of the complex plane C.peerReviewe

Locally convex quasi C∗-normed algebras

AbstractIf A0[‖⋅‖0] is a C∗-normed algebra and τ a locally convex topology on A0 making its multiplication separately continuous, then A0˜[τ] (completion of A0[τ]) is a locally convex quasi ∗-algebra over A0, but it is not necessarily a locally convex quasi ∗-algebra over the C∗-algebra A0˜[‖⋅‖0] (completion of A0[‖⋅‖0]). In this article, stimulated by physical examples, we introduce the notion of a locally convex quasi C∗-normed algebra, aiming at the investigation of A0˜[τ]; in particular, we study its structure, ∗-representation theory and functional calculus

Uniqueness of topology for semisimple lfq-algebras

Various classes of semisimple lmc algebras, among them barrelled Ptak Q-algebras, LF(?-algebras, and F^-algebras, have a uniquely determined topology. © 1993 American Mathematical Society

Structure of contractible locally C*-algebras

A locally C*-algebra is contractible iff it is topologically isomorphic to the topological cartesian product of a certain family of full matrix algebras

Integral representations of linear forms on topological algebras

The article contains no abstrac

The Shirali-Ford theorem as a consequence of Pták theory for hermitian Banach algebras

A simple application of Pták theory for hermitian Banach algebras, combined with a result on normed Q-algebras, gives a non-technical new proof of the Shirali-Ford theorem. A version of this theorem in the setting of non-normed topological algebras is also provided