## Topological algebras with an orthogonal total sequence

### Volume 72 / 1997

Colloquium Mathematicum 72 (1997), 215-222
DOI: 10.4064/cm-72-2-215-222

#### Abstract

The aim of this paper is an investigation of topological algebras with an orthogonal sequence which is total. Closed prime ideals or closed maximal ideals are kernels of multiplicative functionals and the continuous multiplicative functionals are given by the "coefficient functionals". Our main result states that an orthogonal total sequence in a unital Fréchet algebra is already a Schauder basis. Further we consider algebras with a total sequence $(x_n)_{n∈ℕ}$ satisfying $x^2_n=x_n$ and $x_n x_{n+1} = x_{n+1}$ for all n ∈ ℕ.