Orthogonal bases are Schauder bases and a characterization of Φ-algebras
Sherif El-Helaly, Taqdir Husain · Pacific Journal of Mathematics · 1988
It is shown that every orthogonal basis in a topological algebra is a Schauder basis.A new class of topological algebras called Φ-algebras is introduced.They are characterized in terms of seminorms.Among other results, a necessary and sufficient condition for a locally convex 5-algebra with an unconditional orthogonal basis to be an ^(-convex algebra is given.