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Topological algebras with an orthogonal total sequence

100%

Render H.

Colloquium Mathematicum

1997

tom 72

nr 2

215-222

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.

On a problem of Bertram Yood

75%

Abel M., Abel M.

Topological Algebra and its Applications

2014

tom 2

nr 1

In 1964, Bertram Yood posed the following problem: whether the intersection of all closed maximal regular left ideals of a topological ring coincides with the intersection of all closed maximal regular right ideals of this ring. It is proved that these two intersections coincide for advertive and simplicial topological rings and, using this result, it is shown that the topological left radical and the topological right radical for every advertive and simplicial topological algebra coincide.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Topological Algebra and its Applications

1 Abel M.

1 Render H.

1 2014

1 1997

Wyniki wyszukiwania

Topological algebras with an orthogonal total sequence

On a problem of Bertram Yood