Homotonic algebras

Michael Cwikel¹ ; Moshe Goldberg¹

¹ Department of Mathematics Technion – Israel Institute of Technology Haifa 32000, Israel

Studia Mathematica, Tome 195 (2009) no. 3, pp. 287-295

Résumé

An algebra $\mathcal{A}$ of real- or complex-valued functions defined on a set ${\bf T}$ shall be called homotonic if $\mathcal{A}$ is closed under taking absolute values, and for all $f$ and $g$ in $\mathcal{A}$, the product $f\times g$ satisfies $|f\times g|\le|f|\times|g|$. Our main purpose in this paper is two-fold: to show that the above definition is equivalent to an earlier definition of homotonicity, and to provide a simple inequality which characterizes submultiplicativity and strong stability for weighted sup norms on homotonic algebras.

Détail

DOI : 10.4064/sm195-3-7

Mots-clés : algebra mathcal real complex valued functions defined set shall called homotonic mathcal closed under taking absolute values mathcal product times satisfies times times main purpose paper two fold above definition equivalent earlier definition homotonicity provide simple inequality which characterizes submultiplicativity strong stability weighted sup norms homotonic algebras