On the reduced minimum modulus of multiplication operators

Document Type : Original Article

Author

Department of Mathematics, College of Sciences, Yasouj University, Yasouj, Iran

Abstract
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 $R_T$.

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Volume 5, Issue 2
Spring 2024
Pages 29-33

  • Receive Date 04 April 2024
  • Revise Date 09 May 2024
  • Accept Date 15 May 2024