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.
Publié le : 2009-05-15
Classification:
Continuous function algebra,
Boundedness radius,
locally multiplicatively convex topology,
algebra norms in $C(X)$,
46H05,
46J20,
46J40,
46J45
@article{1244038141,
author = {Oubbi, L.},
title = {A Kaplansky-Meyer theorem for subalgebras},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {16},
number = {1},
year = {2009},
pages = { 305-312},
language = {en},
url = {http://dml.mathdoc.fr/item/1244038141}
}
Oubbi, L. A Kaplansky-Meyer theorem for subalgebras. Bull. Belg. Math. Soc. Simon Stevin, Tome 16 (2009) no. 1, pp. 305-312. http://gdmltest.u-ga.fr/item/1244038141/