Topological algebras with an orthogonal total sequence

Render, Hermann

Render, Hermann

Colloquium Mathematicae, Tome 72 (1997), p. 215-222 / Harvested from The Polish Digital Mathematics Library

Résumé

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 ${(x_{n})}_{n \in ℕ}$ satisfying $x_{n}^{2} = x_{n}$ and $x_{n} x_{n + 1} = x_{n + 1}$ for all n ∈ ℕ.

Publié le : 1997-01-01

Zbl 0906.46038

EUDML-ID : urn:eudml:doc:210460

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     author = {Hermann Render},
     title = {Topological algebras with an orthogonal total sequence},
     journal = {Colloquium Mathematicae},
     volume = {72},
     year = {1997},
     pages = {215-222},
     zbl = {0906.46038},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv72i2p215bwm}
}

Render, Hermann. Topological algebras with an orthogonal total sequence. Colloquium Mathematicae, Tome 72 (1997) pp. 215-222. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv72i2p215bwm/

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