Fredholm multiplication operators between Holder spaces

Document Type : Research Articles

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Department of Basic Sciences, Shahid Sattari Aeronautical University of Science and Technology, South Mehrabad, Tehran, Iran.

Abstract

Abstract. Let U be an open bounded subset of $R^d$. We aim to investigate the multiplication operator on Hölder space $C^{1,1}(U)$, specifically focusing on Fredholm operators. Our goal is to provide an interpretation of these operators in these spaces and to discuss and prove their properties. In the case where U is a subset of R, we present and prove results regarding these operators. Furthermore, we establish a necessary condition for the Fredholm property of these operators.

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