Displaying similar documents to “Entire functions and equicontinuity of power maps in Baire algebras.”

Equicontinuity of power maps in locally pseudo-convex algebras

Abdellah El Kinani (2003)

Commentationes Mathematicae Universitatis Carolinae

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We show that, in any unitary (commutative or not) Baire locally pseudo-convex algebra with a continuous product, the power maps are equicontinuous at zero if all entire functions operate. We obtain the same conclusion if every element is bounded. An immediate consequence is a result of A. Arosio on commutative and complete metrizable locally convex algebras.

Discontinuity of the product in multiplier algebras.

Mohamed Oudadess (1990)

Publicacions Matemàtiques

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Entire functions operate in complete locally A-convex algebras but not continuously. Actually squaring is not always continuous. The counterexample we give is multiplier algebra.

Concerning entire functions in B 0 -algebras

W. Żelazko (1994)

Studia Mathematica

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We construct a non-m-convex non-commutative B 0 -algebra on which all entire functions operate. Our example is also a Q-algebra and a radical algebra. It follows that some results true in the commutative case fail in general.

A non-Banach in-convex algebra all of whose closed commutative subalgebras are Banach algebras.

W. Żelazko (1996)

Studia Mathematica

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We construct two examples of complete multiplicatively convex algebras with the property that all their maximal commutative subalgebras and consequently all commutative closed subalgebras are Banach algebras. One of them is non-metrizable and the other is metrizable and non-Banach. This solves Problems 12-16 and 22-24 of [7].

Representation of locally convex algebras.

L. Oubbi (1994)

Revista Matemática de la Universidad Complutense de Madrid

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We deal with the representation of locally convex algebras. On one hand as subalgebras of some weighted space CV(X) and on the other hand, in the case of uniformly A-convex algebras, as inductive limits of Banach algebras. We also study some questions on the spectrum of a locally convex algebra.