Displaying similar documents to “A semitopological algebra without proper closed subalgebras”

On locally bounded algebras

S. Rolewicz (2000)

Banach Center Publications

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It is a survey talk concerning locally bounded algebras.

Topological algebras with an orthogonal total sequence

Hermann Render (1997)

Colloquium Mathematicae

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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 n 2 = x n and x n x n + 1 = x n + 1 for all n ∈ ℕ. ...

On Gelfand-Mazur theorem on a class of F -algebras

E. Anjidani (2014)

Topological Algebra and its Applications

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A topological algebra A is said to be fundamental if there exists b > 1 such that for every sequence (xn) in A, (xn) is Cauchy whenever the sequence bn(xn − xn-1) tends to zero as n → ∞. Let A be a complex unital fundamental F-algebra with bounded elements such that A* separates the points on A. Then we prove that the spectrum σ(a) of every element a ∈ A is nonempty compact. Moreover, if A is a division algebra, then A is isomorphic to the complex numbers ℂ. This result is a generalization...