On denseness of similarity orbits of norm-attainable operators

Abstract

The notion of dense sets has been extensively discussed on both metric and topological spaces. Various properties of the sets have been proved under the underlying spaces. However, if we consider these sets to be from similarity orbits where a topology has been developed on them, little has been done to investigate their denseness. In this paper, we introduce the concept of denseness of similarity orbits of norm-attainable operators in aspect of generalized sets in topological spaces and some of their properties.