Entire functions and -convex structure in commutative Baire algebras.

El Kinani, A.; Oudadess, M.

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Displaying similar documents to “Entire functions and $m$ -convex structure in commutative Baire algebras.”

Entire functions and equicontinuity of power maps in Baire algebras.

Abdellah El Kinani (2000)

Revista Matemática Complutense

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We obtain that the power maps are equicontinuous at zero in any Baire locally convex algebra with a continuous product in which all entire functions operate; whence is m-convex in the commutative case. As a consequence, we get the same result of Mityagin, Rolewicz and Zelazko for commutative B-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.

A non-m-convex algebra on which operate all entire functions

W. Żelazko (1985)

Annales Polonici Mathematici

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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.

Funtional Boundedness of Some M-Complete m-Convex Algebras

M. Oudadess (1997)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

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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].

On the lower hull of convex functions.

Z. Kominek, M. Kuczma (1989)

Aequationes mathematicae

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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.

Displaying similar documents to “Entire functions and m -convex structure in commutative Baire algebras.”

Displaying similar documents to “Entire functions and $m$ -convex structure in commutative Baire algebras.”