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

Bracamonte Mireya, Ereú Jurancy, Marchan Luz

Demonstratio Mathematica

2022

Vol. 55, nr 1

760--771

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