Submultiplicative norms in CC(K)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal C_{\\mathbb C}(\\mathcal K)$$\\end{document} spaces with applications to uniform algebras

Abstract

Certain 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 CC(K)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal C_{\\mathbb C}(\\mathcal K)$$\\end{document} 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.