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Displaying similar documents to “On Local Uniform Topological Algebras”

Topologically Invertible Elements and Topological Spectrum

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Properties of topologically invertible elements and the topological spectrum of elements in unital semitopological algebras are studied. It is shown that the inversion x x - 1 is continuous in every invertive Fréchet algebra, and singly generated unital semitopological algebras have continuous characters if and only if the topological spectrum of the generator is non-empty. Several open problems are presented.

A note on the singular spectrum.

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We compare the singular spectrum of a Banach algebra element with the usual spectrum and exponential spectrum.

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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...

Multipliers of Uniform Topological Algebras

Mohammed El Azhari (2017)

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Let E be a complete uniform topological algebra with Arens-Michael normed factors [...] within an algebra isomorphism ϕ. If each factor Eα is complete, then every multiplier of E is continuous and ϕ is a topological algebra isomorphism where M(E) is endowed with its seminorm topology.