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Example of an algebra which is nontopologizable as a locally convex topological algebra

Author: W. Żelazko
Journal: Proc. Amer. Math. Soc. 110 (1990), 947-949
MSC: Primary 46H05; Secondary 46J05
MathSciNet review: 1012942
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Abstract: Let $ X$ be a real or complex linear space and denote by $ L(X)$ the algebra of all its endomorphisms. We prove that $ L(X)$ is topologizable as a locally convex topological algebra (with jointly continuous multiplication) if and only if it is topologizable as a Banach algebra and this holds if and only if $ X$ is of finite dimension.

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Keywords: Locally convex algebras, topologization of an algebra
Article copyright: © Copyright 1990 American Mathematical Society

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