Operators determining the complete norm topology of C(K)
Volume 124 / 1997
Studia Mathematica 124 (1997), 155-160
DOI: 10.4064/sm-124-2-155-160
Abstract
For any uniformly closed subalgebra A of C(K) for a compact Hausdorff space K without isolated points and $x_{0} ∈ A$, we show that every complete norm on A which makes continuous the multiplication by $x_{0}$ is equivalent to $∥·∥_{∞}$ provided that $x_{0}^{-1}(λ)$ has no interior points whenever λ lies in ℂ. Actually, these assertions are equivalent if A = C(K).
