A Kaplansky-Meyer theorem for subalgebras
L. Oubbi
Source: Bull. Belg. Math. Soc. Simon Stevin Volume 16, Number 2 (2009), 305-312.
Abstract
In this note we show that, for an arbitrary Hausdorff locally m-convex topology on a subalgebra $A$ of the algebra $C(X)$, the boundedness radius $\beta$ is nothing but the uniform norm, whenever $A$ is a $C_b(X)$-module and closed under the complex conjugation. We then deduce a Theorem of Kaplansky-Meyer type for subalgebras.
Primary Subjects: 46H05, 46J20, 46J40, 46J45
Keywords: Continuous function algebra; Boundedness radius; locally multiplicatively convex topology; algebra norms in $C(X)$
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Bulletin of the Belgian Mathematical Society - Simon Stevin
