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.
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In this paper, we study the properties of the multiplication operator acting on the bounded variation space BV[0, 1]. In particular, we show the existence of non-null compact multiplication operators on BV[0, 1] and non-invertible Fredholm multiplication operators on BV[0, 1].
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