Displaying similar documents to “Maximal abelian subalgebras and projections in two Banach algebras associated with a topological dynamical system”

A characterization of maximal regular ideals in lmc algebras

Maria Fragoulopoulou (1992)

Studia Mathematica

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A question of Warner and Whitley concerning a nonunital version of the Gleason-Kahane-Żelazko theorem is considered in the context of nonnormed topological algebras. Among other things it is shown that a closed hyperplane M of a commutative symmetric F*-algebra E with Lindelöf Gel'fand space is a maximal regular ideal iff each element of M belongs to some closed maximal regular ideal of E.

When is L(X) topologizable as a topological algebra?

W. Żelazko (2002)

Studia Mathematica

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Let X be a locally convex space and L(X) be the algebra of all continuous endomorphisms of X. It is known (Esterle [2], [3]) that if L(X) is topologizable as a topological algebra, then the space X is subnormed. We show that in the case when X is sequentially complete this condition is also sufficient. In this case we also obtain some other conditions equivalent to the topologizability of L(X). We also exhibit a class of subnormed spaces X, called sub-Banach spaces, which are not necessarily...