Displaying similar documents to “Representation of locally convex algebras.”

The three-space-problem for locally-m-convex algebras.

Susanne Dierolf, Thomas Heintz (2003)

RACSAM

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We prove that a locally convex algebra A with jointly continuous multiplication is already locally-m-convex, if A contains a two-sided ideal I such that both I and the quotient algebra A/I are locally-m-convex. An application to the behaviour of the associated locally-m-convex topology on ideals is given.

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.

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].