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

Abstract:

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