Geodesic
Topological algebras with an orthogonal total sequence
Colloquium Mathematicum, Tome 72 (1997) no. 2, pp. 215-222.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm-72-2-215-222
Keywords: orthogonal basis, Hadamard product, topological algebra

Hermann Render 1

1 
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Hermann Render. Topological algebras with an orthogonal total sequence. Colloquium Mathematicum, Tome 72 (1997) no. 2, pp. 215-222. doi : 10.4064/cm-72-2-215-222. http://geodesic.mathdoc.fr/articles/10.4064/cm-72-2-215-222/

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