ABSTRACT
A topological algebra is a topological vector space with a jointly continuous multiplication. In the 1970’s, T. Husain and his coworkers started a study of bases in topological algebras. They introduced the following definition to describe the algebraic relations between the basis elements in a topological algebra. This chapter provides a summary of the results pertinent to the Schauderness and unconditionality of orthogonal bases in topological algebras. The study of unconditionality of such bases leads to the concept of Ms-algebras”. The chapter includes various examples of topological algebras with orthogonal bases. It provides special attention to the classification of these algebras into locally m-convex algebras and s-algebras.
