Submultiplicative norms in $$\mathcal C_{\mathbb C}(\mathcal K)$$ spaces with applications to uniform algebras

Abstract

AbstractCertain algebra norms on the algebra of functions on a two-point set are defined and used to construct a new family of parametric algebra norms on the space $$\mathcal C_{\mathbb C}(\mathcal K)$$ C C ( K ) of continuous complex-valued functions on a compact Hausdorff space. As a by-product of our work we transfer our construction to uniform algebras to obtain a new collection of norms with special properties.