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

• Autorzy: W. Żelazko
• Języki publikacji: EN

Abstrakty

EN

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 sequentially complete, but for which the algebra L(X) is normable. Finally we exhibit an example of a subnormed space X for which the algebra L(X) is not topologizable.

Kategorie tematyczne

• 47L10: Algebras of operators on Banach spaces and other topological linear spaces
• 46H35: Topological algebras of operators \SeeMainly{}

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2002
• Tom: 150
• Numer: 3
• Strony: 295-303

Daty

wydano

2002

Twórcy

autor

W. Żelazko

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland

Identyfikatory

DOI

10.4064/sm150-3-6