Multiplication operators on the Banach algebra of bounded Φ-variation functions on compact subsets of ℂ

Abstract

Let AΦ(K){{\mathbb{A}}}_{\Phi }\left({\bf{K}}) be the Banach algebra of bounded Φ\Phi -variation functions defined on a compact set K{\bf{K}} in the complex plane, hh a function defined on K{\bf{K}}, and Mh{M}_{h} a multiplication operator induced by hh. In this article, we determine the conditions that hh must satisfy for Mh{M}_{h} to be an operator that has closed range, finite rank or is compact. We also characterize the conditions that hh must satisfy for Mh{M}_{h} to be a Fredholm operator.

Keywords

• φ-variation
• multiplication operator
• 26a45
• 47b07