We will consider Multiplication operators on Hilbert spaces of analyticfunctions on a domain $\omega \subset \cmark $. We determine the commutants of certainMultiplication operators with adjoints in a Cowen-Douglas class operator.

Please click on PDF to view the 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 $R_T$.

Let M be a lattice module over the multiplicative lattice L. An L-module M is called a Multiplication lattice module if for every element NÎM there exists an element aÎL such that N=a1M. Our objective is to investigate properties of prime elements of Multiplication lattice modules.