On the Deddens algebras of a class of bounded operators

In this paper, we investigate the relation between the Deddens and spectral radius algebras of two bounded linear operators, noting a similarity between them. Additionally, we characterize the Deddens and spectral radius algebras related to rank one operators, operators that are similar to rank one operators, operators that are majorized by rank one operators, and quasi-isometry operators. Furthermore, we apply these results to the class of weighted conditional type operators on the Hilbert space $L^2(\mu)$.