Hamid Rezaei - Department of Mathematics, College of Sciences, Yasouj University, Yasouj, Iran

In this paper, we investigate the properties of the reduced minimum modulus in the context of Banach spaces. Given a Banach space X, we denote the algebra of bounded operators on X as B(X). Our primary focus is on examining the relationship between the reduced minimum modulus of a given operator T \in B(X) and its associated left and right multiplication operators, denoted by L_T: S \mapsto TS and R_T: S \mapsto ST, respectively. By analyzing these relationships, we present a comprehensive analysis of their properties and derive novel results concerning the reduced minimum modulus of L_T and R_T.

closed range operator, Reduced minimum modulus, Multiplication operator