Further radii in topological algebras
Lahbib Oubbi · Bulletin of the Belgian Mathematical Society - Simon Stevin · 2002
We introduce two new radii in general topological algebras.The first one, η, plays a role similar to that of the norm in Banach algebras in the sense that the seriesx n converges whenever η(x) < 1.The second one permits, among others, to give new expressions of the spectral radius ρ and the boundedness radius β in a non-commutative locally m-convex algebra.Finally, we show that, in contrast to the locally convex setting, β need not be dominated by ρ in a topological (even F-) algebra with continuous inversion.