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Orthogonal bases are Schauder bases and a characterization of Φ-algebras

1988; Mathematical Sciences Publishers; Volume: 132; Issue: 2 Linguagem: Inglês

10.2140/pjm.1988.132.265

1945-5844

Sherif El-Helaly, Taqdir Husain,

Advanced Algebra and Logic

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.